A variational proof of Alexandrov's convex cap theorem

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We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we prove that generalized convex caps with the fixed boundary are globally rigid, that is uniquely determined by their curvatures.
28 pages, 7 figures Minor changes in the introduction, Subsection 4.3 added, references added

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Differential Geometry, Metric Geometry, 52B10, 53C45; 52C25

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http://salesiana.dossiersoluciones.com/handle/123456789/127815

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703169
 http://arxiv.org/abs/math/0703169

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arXiv