Lectures on Minimal Surfaces in R3
Author : Yi Fang
Publisher :
Page : 192 pages
File Size : 43,81 MB
Release : 1996
Category : Geometry, Differential
ISBN :
A Course in Minimal Surfaces
Author : Tobias Holck Colding
Publisher : American Mathematical Society
Page : 330 pages
File Size : 41,42 MB
Release : 2024-01-18
Category : Mathematics
ISBN : 1470476401
Book Description
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.
Minimal Surfaces in R 3
Author : J.Lucas M. Barbosa
Publisher : Springer
Page : 133 pages
File Size : 47,36 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540398309
Book Description
Lectures on Minimal Surfaces: Introduction, fundamentals, geometry and basic boundary value problems
Author : Johannes C. C. Nitsche
Publisher :
Page : 563 pages
File Size : 12,49 MB
Release : 1989
Category : Mathematics
ISBN : 9780521244275
Book Description
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.
Minimal Surfaces from a Complex Analytic Viewpoint
Author : Antonio Alarcón
Publisher : Springer Nature
Page : 430 pages
File Size : 10,62 MB
Release : 2021-03-10
Category : Mathematics
ISBN : 3030690563
Book Description
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.
Lectures on Symplectic Geometry
Author : Ana Cannas da Silva
Publisher : Springer
Page : 240 pages
File Size : 22,82 MB
Release : 2004-10-27
Category : Mathematics
ISBN : 354045330X
Book Description
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
The Global Theory of Minimal Surfaces in Flat Spaces
Author : W.H. III Meeks
Publisher : Springer
Page : 126 pages
File Size : 12,25 MB
Release : 2004-10-11
Category : Mathematics
ISBN : 3540456090
Book Description
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.
Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935
Author : United States. Securities and Exchange Commission
Publisher :
Page : 802 pages
File Size : 26,76 MB
Release : 1998
Category : Securities
ISBN :
Book Description
Complete and Compact Minimal Surfaces
Author : Kichoon Yang
Publisher : Springer Science & Business Media
Page : 185 pages
File Size : 16,83 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9400910150
Book Description
'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.
Lectures on Classical Differential Geometry
Author : Dirk J. Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 40,82 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486138186
Book Description
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.
