| 书目名称 | Constant Mean Curvature Surfaces with Boundary | | 编辑 | Rafael López | | 视频video | | | 概述 | Includes set of interesting open problems.First comprehensive publication on "compact surfaces with boundary".Gives a state-of-the-art review of the theory.Includes supplementary material: | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | .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 | | 出版日期 | Book 2013 | | 关键词 | 53, 53A, 53A10, 53C42, 35J, 35J60; Dirichlet problem; flux formula; mean curvature; tangency principle; p | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-39626-7 | | isbn_softcover | 978-3-662-51256-2 | | isbn_ebook | 978-3-642-39626-7Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer-Verlag Berlin Heidelberg 2013 |
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发表于 2025-3-21 20:09:15
