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Author : H. Blaine Lawson
Publisher : Unknown
Page : 200 pages
File Size : 48,8 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015014355195
Author : Herbert Blaine Lawson
Publisher : Unknown
Page : 128 pages
File Size : 47,7 Mb
Release : 1980
Category : Electronic
ISBN : OCLC:834172073
Author : Leon Melvin Simon
Publisher : Unknown
Page : 57 pages
File Size : 53,7 Mb
Release : 1980
Category : Submanifolds
ISBN : 0868390984
Author : Y. L. Xin
Publisher : World Scientific
Page : 271 pages
File Size : 55,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812386878
The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Author : Enrico Bombieri
Publisher : Princeton University Press
Page : 368 pages
File Size : 40,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881437
The description for this book, Seminar On Minimal Submanifolds. (AM-103), Volume 103, will be forthcoming.
Author : Kichoon Yang
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 40,5 Mb
Release : 1989-09-30
Category : Mathematics
ISBN : 0792303997
'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.
Author : Tobias H. Colding,William P. Minicozzi
Publisher : Courant Institute of Mathemetical Sciences
Page : 136 pages
File Size : 51,5 Mb
Release : 1999
Category : Mathematics
ISBN : STANFORD:36105021943365
Author : Henri Anciaux
Publisher : World Scientific
Page : 184 pages
File Size : 42,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814291248
Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. For the first time, this textbook provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Khler manifolds are given.
Author : Yi Fang
Publisher : Unknown
Page : 192 pages
File Size : 42,8 Mb
Release : 1996
Category : Geometry, Differential
ISBN : UOM:39015047096311
Author : Franki Dillen,Leopold Verstraelen
Publisher : World Scientific
Page : 298 pages
File Size : 51,8 Mb
Release : 1992-07-17
Category : Electronic
ISBN : 9789814554626
This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.
Author : Shiing-Shen Chern
Publisher : Unknown
Page : 68 pages
File Size : 42,5 Mb
Release : 1968
Category : Minimal submanifolds
ISBN : UOM:39015049076907
Author : Frank Morgan
Publisher : Academic Press
Page : 264 pages
File Size : 55,6 Mb
Release : 2008-09-09
Category : Mathematics
ISBN : 0080922406
Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers. This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincaré Conjecture. This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject. New to the 4th edition: * Abundant illustrations, examples, exercises, and solutions. * The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori." * A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture." * Contributions by undergraduates.
Author : Richard S. Palais,Chuu-lian Terng
Publisher : Springer
Page : 276 pages
File Size : 44,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459965
Author : Tobias H. Colding,William P. Minicozzi
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 55,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853238
"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."--Publisher's description.
Author : W.H. III Meeks,A. Ros,H. Rosenberg
Publisher : Springer
Page : 124 pages
File Size : 44,8 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.
