Direchlets Principle Conformal Mapping And Minimal Surfaces

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Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces

Author : R. Courant
Publisher : Springer Science & Business Media
ISBN 13 : 1461299179
Total Pages : 340 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces by : R. Courant

Download or read book Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces written by R. Courant and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods of more general significance. The present book deals with subjects of this category. It is written in a style which, as the author hopes, expresses adequately the balance and tension between the individuality of mathematical objects and the generality of mathematical methods. The author has been interested in Dirichlet's Principle and its various applications since his days as a student under David Hilbert. Plans for writing a book on these topics were revived when Jesse Douglas' work suggested to him a close connection between Dirichlet's Principle and basic problems concerning minimal sur faces. But war work and other duties intervened; even now, after much delay, the book appears in a much less polished and complete form than the author would have liked."

Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces

Author : Richard Courant (Mathematiker, Deutschland, USA)
Publisher :
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.:/5 (888 download)

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Book Synopsis Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces by : Richard Courant (Mathematiker, Deutschland, USA)

Download or read book Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces written by Richard Courant (Mathematiker, Deutschland, USA) and published by . This book was released on 1950 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces

Author : Richard Courant
Publisher :
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces by : Richard Courant

Download or read book Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces written by Richard Courant and published by . This book was released on 1967 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dirichlet's Principle, Conformal Mapping, and Mapping and Minimal Surfaces

Author : Richard Courant
Publisher :
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.:/5 (222 download)

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Book Synopsis Dirichlet's Principle, Conformal Mapping, and Mapping and Minimal Surfaces by : Richard Courant

Download or read book Dirichlet's Principle, Conformal Mapping, and Mapping and Minimal Surfaces written by Richard Courant and published by . This book was released on 1950 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dirichlet's Principle, Conformal Mapping and Minimal Surfaces

Author : Menahem Max Schiffer
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.:/5 (459 download)

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Book Synopsis Dirichlet's Principle, Conformal Mapping and Minimal Surfaces by : Menahem Max Schiffer

Download or read book Dirichlet's Principle, Conformal Mapping and Minimal Surfaces written by Menahem Max Schiffer and published by . This book was released on 1950 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dirichlet S Principle, Conformal Mapping and Minim Al Surfaces

Author : Courant
Publisher :
ISBN 13 : 9780470178867
Total Pages : 344 pages
Book Rating : 4.1/5 (788 download)

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Book Synopsis Dirichlet S Principle, Conformal Mapping and Minim Al Surfaces by : Courant

Download or read book Dirichlet S Principle, Conformal Mapping and Minim Al Surfaces written by Courant and published by . This book was released on 1950-01-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry V

Author : Robert Osserman
Publisher : Springer Science & Business Media
ISBN 13 : 3662034840
Total Pages : 279 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Geometry V by : Robert Osserman

Download or read book Geometry V written by Robert Osserman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few people outside of mathematics are aware of the varieties of mathemat ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.

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.

Direchlet's Principle, Conformal Mapping and Minimal Surfaces

Author : Richard Courant
Publisher :
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.:/5 (643 download)

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Book Synopsis Direchlet's Principle, Conformal Mapping and Minimal Surfaces by : Richard Courant

Download or read book Direchlet's Principle, Conformal Mapping and Minimal Surfaces written by Richard Courant and published by . This book was released on 1950 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Minimal Surfaces

Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3642116981
Total Pages : 699 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Minimal Surfaces by : Ulrich Dierkes

Download or read book Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Björling ́s initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau ́s problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche ́s uniqueness theorem and Tomi ́s finiteness result. In addition, a theory of unstable solutions of Plateau ́s problems is developed which is based on Courant ́s mountain pass lemma. Furthermore, Dirichlet ́s problem for nonparametric H-surfaces is solved, using the solution of Plateau ́s problem for H-surfaces and the pertinent estimates.

Dirichlet's Principle

Author : A. F. Monna
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.:/5 (25 download)

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Book Synopsis Dirichlet's Principle by : A. F. Monna

Download or read book Dirichlet's Principle written by A. F. Monna and published by . This book was released on 1975 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Mapping

Author : Zeev Nehari
Publisher : Courier Corporation
ISBN 13 : 0486145034
Total Pages : 418 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Conformal Mapping by : Zeev Nehari

Download or read book Conformal Mapping written by Zeev Nehari and published by Courier Corporation. This book was released on 2012-05-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the complex integral calculus, and families of analytic functions. Included here are discussions of Green's formula, the Poisson formula, the Cauchy-Riemann equations, Cauchy's theorem, the Laurent series, and the Residue theorem. The final three chapters consider in detail conformal mapping of simply-connected domains, mapping properties of special functions, and conformal mapping of multiply-connected domains. The coverage here includes such topics as the Schwarz lemma, the Riemann mapping theorem, the Schwarz-Christoffel formula, univalent functions, the kernel function, elliptic functions, univalent functions, the kernel function, elliptic functions, the Schwarzian s-functions, canonical domains, and bounded functions. There are many problems and exercises, making the book useful for both self-study and classroom use. The author, former professor of mathematics at Carnegie-Mellon University, has designed the book as a semester's introduction to functions of a complex variable followed by a one-year graduate course in conformal mapping. The material is presented simply and clearly, and the only prerequisite is a good working knowledge of advanced calculus.

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.

Elements of the geometry and topology of minimal surfaces in three-dimensional space

Author : A. T. Fomenko
Publisher : American Mathematical Soc.
ISBN 13 : 0821837915
Total Pages : 156 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Elements of the geometry and topology of minimal surfaces in three-dimensional space by : A. T. Fomenko

Download or read book Elements of the geometry and topology of minimal surfaces in three-dimensional space written by A. T. Fomenko and published by American Mathematical Soc.. This book was released on 2005 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9400959915
Total Pages : 555 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Harmonic Maps

Author : James Eells
Publisher : World Scientific
ISBN 13 : 9789810207045
Total Pages : 472 pages
Book Rating : 4.2/5 (7 download)

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Book Synopsis Harmonic Maps by : James Eells

Download or read book Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1992 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.

Constantin Carathéodory

Author : Maria Georgiadou
Publisher : Springer Science & Business Media
ISBN 13 : 3642185622
Total Pages : 667 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Constantin Carathéodory by : Maria Georgiadou

Download or read book Constantin Carathéodory written by Maria Georgiadou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: With breathtaking detail, Maria Georgiadou sheds light on the work and life of Constantin Carathéodory, who until now has been ignored by historians. In her thought-provoking book, Georgiadou maps out the mathematician’s oeuvre, life and turbulent historical surroundings. Descending from the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a lifetime to mathematics and education. He significantly contributed to: calculus of variations, the theory of point set measure, the theory of functions of a real variable, pdes, and complex function theory. An exciting and well-written biography, once started, difficult to put down.