Nonlocal Perimeter Curvature And Minimal Surfaces For Measurable Sets

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Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets

Author : José M. Mazón
Publisher : Springer
ISBN 13 : 3030062430
Total Pages : 123 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets by : José M. Mazón

Download or read book Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets written by José M. Mazón and published by Springer. This book was released on 2019-04-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.

Minimal Surfaces and Functions of Bounded Variation

Author : Giusti
Publisher : Springer Science & Business Media
ISBN 13 : 1468494864
Total Pages : 250 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Minimal Surfaces and Functions of Bounded Variation by : Giusti

Download or read book Minimal Surfaces and Functions of Bounded Variation written by Giusti and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].

Functions of Least Gradient

Author : Wojciech Górny
Publisher : Springer Nature
ISBN 13 : 3031518810
Total Pages : 442 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Functions of Least Gradient by : Wojciech Górny

Download or read book Functions of Least Gradient written by Wojciech Górny and published by Springer Nature. This book was released on with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sobolev Maps to the Circle

Author : Haim Brezis
Publisher : Springer Nature
ISBN 13 : 1071615122
Total Pages : 552 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Sobolev Maps to the Circle by : Haim Brezis

Download or read book Sobolev Maps to the Circle written by Haim Brezis and published by Springer Nature. This book was released on 2022-01-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The “Complements and Open Problems” sections provide short introductions to various subsequent developments or related topics, and suggest newdirections of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.

Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness

Author : Serena Dipierro
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (962 download)

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Book Synopsis Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness by : Serena Dipierro

Download or read book Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness written by Serena Dipierro and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior regularity and rigidity properties, in a quantitative and qualitative way, and their (perhaps rather surprising) boundary behavior. We present at least a sketch of the proofs of these results, in a way that aims to be as elementary and self contained as possible, referring to the papers [CRS10, SV13, CV13, BFV14,FV, DSV15,CSV16] for full details.

A Survey of Minimal Surfaces

Author : Robert Osserman
Publisher : Courier Corporation
ISBN 13 : 0486649989
Total Pages : 226 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis A Survey of Minimal Surfaces by : Robert Osserman

Download or read book A Survey of Minimal Surfaces written by Robert Osserman and published by Courier Corporation. This book was released on 1986-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This clear and comprehensive study features 12 sections that discuss parametric and non-parametric surfaces, surfaces that minimize area, isothermal parameters, Bernstein's theorem, minimal surfaces with boundary, and many other topics. This revised edition includes material on minimal surfaces in relativity and topology and updated work on Plateau's problem and isoperimetric inequalities. 1969 edition.

Regularity of Minimal Surfaces

Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3642117007
Total Pages : 634 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Regularity of Minimal Surfaces by : Ulrich Dierkes

Download or read book Regularity of Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau ́s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau ́s problem have no interior branch points.

A Course in Minimal Surfaces

Author : Tobias Holck Colding
Publisher : American Mathematical Society
ISBN 13 : 1470476401
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Course in Minimal Surfaces by : Tobias Holck Colding

Download or read book A Course in Minimal Surfaces written by Tobias Holck Colding and published by American Mathematical Society. This book was released on 2024-01-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

Complete and Compact Minimal Surfaces

Author : Kichoon Yang
Publisher : Springer Science & Business Media
ISBN 13 : 9780792303992
Total Pages : 198 pages
Book Rating : 4.3/5 (39 download)

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Book Synopsis Complete and Compact Minimal Surfaces by : Kichoon Yang

Download or read book Complete and Compact Minimal Surfaces written by Kichoon Yang and published by Springer Science & Business Media. This book was released on 1989-09-30 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ... , si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Minimal Surfaces from a Complex Analytic Viewpoint

Author : Antonio Alarcón
Publisher : Springer Nature
ISBN 13 : 3030690563
Total Pages : 430 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Minimal Surfaces from a Complex Analytic Viewpoint by : Antonio Alarcón

Download or read book Minimal Surfaces from a Complex Analytic Viewpoint written by Antonio Alarcón and published by Springer Nature. This book was released on 2021-03-10 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.

Minimal Surfaces II

Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3662087766
Total Pages : 435 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Minimal Surfaces II by : Ulrich Dierkes

Download or read book Minimal Surfaces II written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.

Complete Minimal Surfaces of Finite Total Curvature

Author : Kichoon Yang
Publisher : Springer
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Complete Minimal Surfaces of Finite Total Curvature by : Kichoon Yang

Download or read book Complete Minimal Surfaces of Finite Total Curvature written by Kichoon Yang and published by Springer. This book was released on 1994-07-31 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on the idea that the study of complete minimal surfaces in R3 of finite total curvature amounts to the study of linear series on algebraic curves. A detailed account of the Puncture Number Problem, which seeks to determine all possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature, is given here for the first time in book form. Several recent results on the puncture number problem are given along with numerous examples. The emphasis is on manufacturing minimal surfaces from a given Riemann surface using the theory of divisions and residue calculus. Relevant results from algebraic geometry are collected in Chapter 1, which makes the book nearly self-contained. A brief survey of minimal surface theory in general is given in Chapter 2. Chapter 3 includes Mo's recent moduli construction. For graduate students and research mathematicians in differential geometry, function theory and algebraic curves, as well as for those working in materials science or crystallography.

Nonlocal Diffusion and Applications

Author : Claudia Bucur
Publisher : Springer
ISBN 13 : 3319287397
Total Pages : 165 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Nonlocal Diffusion and Applications by : Claudia Bucur

Download or read book Nonlocal Diffusion and Applications written by Claudia Bucur and published by Springer. This book was released on 2016-04-08 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.

Computing Minimal Surfaces Via Level Set Curvature Flow

Author : David Layne Chopp
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.:/5 (33 download)

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Book Synopsis Computing Minimal Surfaces Via Level Set Curvature Flow by : David Layne Chopp

Download or read book Computing Minimal Surfaces Via Level Set Curvature Flow written by David Layne Chopp and published by . This book was released on 1991 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Measure Theory and Fine Properties of Functions, Revised Edition

Author : Lawrence Craig Evans
Publisher : CRC Press
ISBN 13 : 1482242397
Total Pages : 314 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Measure Theory and Fine Properties of Functions, Revised Edition by : Lawrence Craig Evans

Download or read book Measure Theory and Fine Properties of Functions, Revised Edition written by Lawrence Craig Evans and published by CRC Press. This book was released on 2015-04-17 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the p- theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.

Physics of Surfaces and Interfaces

Author : Harald Ibach
Publisher : Springer Science & Business Media
ISBN 13 : 3540347100
Total Pages : 653 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Physics of Surfaces and Interfaces by : Harald Ibach

Download or read book Physics of Surfaces and Interfaces written by Harald Ibach and published by Springer Science & Business Media. This book was released on 2006-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook covers the major developments in surface sciences of recent decades, from experimental tricks and basic techniques to the latest experimental methods and theoretical understanding. It is unique in its attempt to treat the physics of surfaces, thin films and interfaces, surface chemistry, thermodynamics, statistical physics and the physics of the solid/electrolyte interface in an integral manner, rather than in separate compartments. It is designed as a handbook for the researcher as well as a study-text for graduate students. Written explanations are supported by 350 graphs and illustrations.