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Titlebook: Constant Mean Curvature Surfaces with Boundary; Rafael López Book 2013 Springer-Verlag Berlin Heidelberg 2013 53, 53A, 53A10, 53C42, 35J,

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發(fā)表于 2025-3-21 20:09:15 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Constant Mean Curvature Surfaces with Boundary
編輯Rafael López
視頻videohttp://file.papertrans.cn/236/235840/235840.mp4
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:
叢書名稱Springer Monographs in Mathematics
圖書封面Titlebook: Constant Mean Curvature Surfaces with Boundary;  Rafael López Book 2013 Springer-Verlag Berlin Heidelberg 2013 53, 53A, 53A10, 53C42, 35J,
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
關(guān)鍵詞53, 53A, 53A10, 53C42, 35J, 35J60; Dirichlet problem; flux formula; mean curvature; tangency principle; p
版次1
doihttps://doi.org/10.1007/978-3-642-39626-7
isbn_softcover978-3-662-51256-2
isbn_ebook978-3-642-39626-7Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag Berlin Heidelberg 2013
The information of publication is updating

書目名稱Constant Mean Curvature Surfaces with Boundary影響因子(影響力)




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沙發(fā)
發(fā)表于 2025-3-21 23:01:29 | 只看該作者
Surfaces with Constant Mean Curvature,arise as solutions of a variational problem associated to the area functional and related with the classical isoperimetric problem. We state the first and second variation formula for the area and we give the notion of stability of a cmc surface. Next, we introduce the complex analysis as a basic to
板凳
發(fā)表于 2025-3-22 02:57:22 | 只看該作者
地板
發(fā)表于 2025-3-22 06:44:01 | 只看該作者
Constant Mean Curvature Embedded Surfaces,e context of embedded surfaces, this problem may be partially answered using the reflection technique of Alexandrov. With this method we will give conditions whether the symmetries of the boundary are inherited to the surface, in particular, when the boundary is a plane curve. We employ the method o
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發(fā)表于 2025-3-22 17:45:44 | 只看該作者
Constant Mean Curvature Disks with Circular Boundary, is umbilical under the assumption of embeddedness. In this chapter we shall consider that the topology of the surface is the simplest one, say, a disk. We shall prove that if a cmc disk immersed in . spans a circle and its area is less than or equal to of a spherical cap with the same mean curvatur
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發(fā)表于 2025-3-22 22:21:58 | 只看該作者
The Dirichlet Problem of the cmc Equation,mates of Ladyzhenskaya and Uraltseva, the existence of the Dirichlet problem reduces to the question of obtaining a priori estimates for the solution and its gradient. The purpose of the present chapter is to study the geometry that lies behind the Dirichlet problem, giving a geometric approach to t
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發(fā)表于 2025-3-23 01:42:25 | 只看該作者
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發(fā)表于 2025-3-23 09:09:25 | 只看該作者
Constant Mean Curvature Surfaces in Hyperbolic Space,n Euclidean space, there are some differences, emphasizing the variety of umbilical surfaces of?. because besides totally geodesic surfaces and spheres, there are equidistant surfaces and horospheres. We shall investigate if the umbilical surfaces are the only possible examples with boundary a circl
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