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portada Constant Mean Curvature Surfaces With Boundary (Springer Monographs in Mathematics)
Type
Physical Book
Publisher
Author
Language
English
Pages
306
Format
Hardcover
ISBN13
9783642396250
Edition No.
2013th

Constant Mean Curvature Surfaces With Boundary (Springer Monographs in Mathematics)

Rafael López (Author) · Springer · Hardcover

Constant Mean Curvature Surfaces With Boundary (Springer Monographs in Mathematics) - Rafael López

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Synopsis "Constant Mean Curvature Surfaces With Boundary (Springer Monographs in Mathematics)"

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.

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