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Author : Luc Pétiard
Publisher :
ISBN 13 :
Total Pages : 65 pages
Book Rating : 4.:/5 (113 download)
Download or read book Isoperimetric Inequalities for Laplace and Steklov Problems on Riemannian Manifolds written by Luc Pétiard and published by . This book was released on 2019 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mikhail Karpukhin
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (18 download)
Download or read book Isoperimetric Inequalities for Laplace and Steklov Eigenvalues written by Mikhail Karpukhin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Isoperimetric inequalities for eigenvalues of geometric operators have received a lot of attention in recent years. Such inequalities are of particular interest for the eigenvalues of Laplace and Dirichlet-to-Neumann operators on Riemannian manifolds, where they exhibit a surprising connection to the theory of minimal submanifolds. This bridge between analysis and geometry provides a path to solving problems from both fields. In the present manuscript we apply geometric methods to prove several new isoperimetric inequalities. In particular, we obtain an isoperimetric inequality for the first Laplace eigenvalue on non-orientable surfaces, improving upon results of P. Li and S.-T. Yau. We prove an isoperimetric inequality for all Steklov eigenvalues on orientable surfaces, improving upon results of A. Girouard and I. Polterovich. We also provide a high-dimensional analog of the latter inequality by considering Dirichlet-to-Neumann operators on differential forms. Finally, jointly with N. Nadirashvili, A. Penskoi and I. Polterovich we establish a sharp inequality for all Laplace eigenvalues on a two-dimensional sphere settling the conjecture of Nadirashvili proposed in 2002." --
Author : Isaac Chavel
Publisher : Cambridge University Press
ISBN 13 : 9780521802673
Total Pages : 292 pages
Book Rating : 4.8/5 (26 download)
Download or read book Isoperimetric Inequalities written by Isaac Chavel and published by Cambridge University Press. This book was released on 2001-07-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
ISBN 13 : 303650298X
Total Pages : 208 pages
Book Rating : 4.0/5 (365 download)
Download or read book Inequalities in Geometry and Applications written by Gabriel-Eduard Vîlcu and published by MDPI. This book was released on 2021-03-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.
Author : Catherine Bandle
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.3/5 (91 download)
Download or read book Isoperimetric Inequalities and Applications written by Catherine Bandle and published by Pitman Publishing. This book was released on 1980 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Levitin
Publisher : American Mathematical Society
ISBN 13 : 1470475251
Total Pages : 346 pages
Book Rating : 4.4/5 (74 download)
Download or read book Topics in Spectral Geometry written by Michael Levitin and published by American Mathematical Society. This book was released on 2023-11-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.
Author : Pierre H. Berard
Publisher : Springer
ISBN 13 : 3540409580
Total Pages : 284 pages
Book Rating : 4.5/5 (44 download)
Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Menahem Schiffer
Publisher : Courier Corporation
ISBN 13 : 0486795438
Total Pages : 465 pages
Book Rating : 4.4/5 (867 download)
Download or read book Functionals of Finite Riemann Surfaces written by Menahem Schiffer and published by Courier Corporation. This book was released on 2014-06-01 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph on finite Riemann surfaces, based on the authors' 1949–50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of "a plethora of ideas, each interesting in its own right," noting that "the patient reader will be richly rewarded." Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theorems for finite Riemann surfaces, and relations between differentials. Subsequent chapters explore bilinear differentials, surfaces imbedded in a given surface, integral operators, and variations of surfaces and of their functionals. The book concludes with a look at applications of the variational method and remarks on generalization to higher dimensional Kahler manifolds.
Author : Filippo Gazzola
Publisher : Springer
ISBN 13 : 3642122450
Total Pages : 444 pages
Book Rating : 4.6/5 (421 download)
Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer. This book was released on 2010-05-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
Author : José Fernando Escobar
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.E/5 ( download)
Download or read book Some Variational Problems in Geometry written by José Fernando Escobar and published by . This book was released on 2000 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierre de la Harpe
Publisher : University of Chicago Press
ISBN 13 : 9780226317199
Total Pages : 320 pages
Book Rating : 4.3/5 (171 download)
Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-10-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
Author : Sheldon Axler
Publisher : Springer Science & Business Media
ISBN 13 : 1475781377
Total Pages : 266 pages
Book Rating : 4.4/5 (757 download)
Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
Author : Nachman Aronszajn
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (44 download)
Download or read book Polyharmonic Functions written by Nachman Aronszajn and published by Oxford University Press, USA. This book was released on 1983 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Patrizia Pucci
Publisher : Springer Science & Business Media
ISBN 13 : 3764381450
Total Pages : 240 pages
Book Rating : 4.7/5 (643 download)
Download or read book The Maximum Principle written by Patrizia Pucci and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
Author : Piero Villaggio
Publisher : Cambridge University Press
ISBN 13 : 9780521573245
Total Pages : 694 pages
Book Rating : 4.5/5 (732 download)
Download or read book Mathematical Models for Elastic Structures written by Piero Villaggio and published by Cambridge University Press. This book was released on 1997-10-28 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.
Author : Bo’az Klartag
Publisher : American Mathematical Soc.
ISBN 13 : 1470425424
Total Pages : 90 pages
Book Rating : 4.4/5 (74 download)
Download or read book Needle Decompositions in Riemannian Geometry written by Bo’az Klartag and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Author : Alexandre Girouard
Publisher : American Mathematical Soc.
ISBN 13 : 147042665X
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometric and Computational Spectral Theory written by Alexandre Girouard and published by American Mathematical Soc.. This book was released on 2017-10-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and Centre de Recherches Mathématiques The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Séminaire de Mathématiques Supérieures on Geometric and Computational Spectral Theory, held from June 15–26, 2015, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.
