Constant Mean Curvature Surfaces with Boundary

種類:

電子ブック

責任表示:

by Rafael López

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013

著者名:

• López, Rafael
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783642396267 [3642396267]    

注記:

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 exposit

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