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Author : Yi Fang
Publisher : Unknown
Page : 192 pages
File Size : 44,5 Mb
Release : 1996
Category : Geometry, Differential
ISBN : UOM:39015047096311
Author : Johannes C. C. Nitsche
Publisher : Unknown
Page : 563 pages
File Size : 46,9 Mb
Release : 1989
Category : Mathematics
ISBN : 0521244277
This book is a revised and translated version of the first five chapters of Vorlesungen ^D"uber Minimalfl^D"achen. It deals with the parametric minimal surface in Euclidean space. The author presents a broad survey that extends from the classical beginnings to the current situation while highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks.
Author : H. Blaine Lawson
Publisher : Unknown
Page : 200 pages
File Size : 40,5 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015014355195
Author : Tobias H. Colding,William P. Minicozzi
Publisher : Courant Institute of Mathemetical Sciences
Page : 136 pages
File Size : 46,7 Mb
Release : 1999
Category : Mathematics
ISBN : STANFORD:36105021943365
Author : W.H. III Meeks,A. Ros,H. Rosenberg
Publisher : Springer
Page : 124 pages
File Size : 46,9 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540456094
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
Author : Johannes C. C. Nitsche
Publisher : Cambridge University Press
Page : 0 pages
File Size : 49,6 Mb
Release : 2011-03-03
Category : Mathematics
ISBN : 0521137780
This 1989 monograph deals with parametric minimal surfaces in Euclidean space. The author presents a broad survey which extends from the classical beginnings to the current situation whilst highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks. The presentation is complete and is complemented by a bibliography of nearly 1600 references. The careful expository style and emphasis on geometric aspects are extremely valuable. Moreover, in the years leading up to the publication of this book, the theory of minimal surfaces was finding increasing application to other areas of mathematics and the physical sciences ensuring that this account will appeal to non-specialists as well.
Author : Johannes C. C. Nitsche
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 1989
Category : Electronic
ISBN : OCLC:471837598
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,8 Mb
Release : 1996
Category : Electronic
ISBN : 0731524446
Author : E. Bombieri
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 41,6 Mb
Release : 2011-06-04
Category : Mathematics
ISBN : 9783642109706
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi’s measure and thin obstacles.
Author : Giusti
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 43,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781468494860
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].
Author : Tobias Holck Colding,William P. Minicozzi II
Publisher : American Mathematical Society
Page : 330 pages
File Size : 44,7 Mb
Release : 2024-01-18
Category : Mathematics
ISBN : 9781470476403
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.
Author : Herbert Blaine Lawson
Publisher : Unknown
Page : 128 pages
File Size : 48,8 Mb
Release : 1980
Category : Electronic
ISBN : OCLC:834172073
Author : Dirk J. Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 51,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138183
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 499 pages
File Size : 43,7 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107153042
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Author : Anthony Tromba
Publisher : Birkhäuser
Page : 224 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886130
These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.