عنوان

Constant mean curvature surfaces with boundary /

(Number (ISBN

3642396267 (electronic bk.)

(Number (ISBN

9783642396267 (electronic bk.)

Erroneous ISBN

9783642396250

Number

dltt

Title Proper

Constant mean curvature surfaces with boundary /

General Material Designation

[Book]

First Statement of Responsibility

Rafael López

Specific Material Designation and Extent of Item

1 online resource (xiv, 292 pages) :

Other Physical Details

illustrations

Series Title

Springer monographs in mathematics,

ISSN of Series

1439-7382

Text of Note

Includes bibliographical references and index

Text of Note

Surfaces with Constant Mean Curvature -- Constant Mean Curvature Embedded Surfaces.-The Flux Formula for Constant Mean Curvature Surfaces -- The Area and the Volume of a Constant Mean Curvature Surface -- Constant Mean Curvature Discs with Circular Boundary -- The Dirichlet Problem of the CMC Equation -- The Dirichlet Problem in Unbounded Domains -- Constant Mean Curvature Surfaces in Hyperbolic Space -- The Dirichlet Problem in Hyperbolic Space -- Constant Mean Curvature Surfaces in Lorentz-Minkowski Space -- Appendix: A. The Variation Formula of the Area and the Volume -- B.Open Questions

0

Text of Note

The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of "compact surfaces with boundaries," narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case; and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems

Title

OhioLINK electronic book center (Online)

Title

SpringerLink

Boundary value problems

Curves, Algebraic

Surfaces of constant curvature

MAT-- 012000

MAT012030

PBMP

Number

Edition

Class number

Class number

Lopez, Rafael

Ohio Library and Information Network

Date of Transaction

20131202122225.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y