A variational proof of Alexandrov's convex cap theorem

Details A variational proof of Alexandrov's convex cap theorem A variational proof of Alexandrov's convex cap theorem

2007-03-06

arxiv.org/abs/math/0703169v2

Mathematics

Differential Geometry

28 pages, 7 figures Minor changes in the introduction, Subsection 4.3 added, references added

Scientific paper

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.

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