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- W2802121752 abstract "We prove that any properly oriented $C^{2,1}$ isometric immersion of a positively curved Riemannian surface M into Euclidean 3-space is uniquely determined, up to a rigid motion, by its values on any curve segment in M. A generalization of this result to nonnegatively curved surfaces is presented as well under suitable conditions on their parabolic points. Thus we obtain a local version of Cohn-Vossen's rigidity theorem for convex surfaces subject to a Dirichlet condition. The proof employs in part Hormander's unique continuation principle for elliptic PDEs. Our approach also yields a short proof of Cohn-Vossen's theorem." @default.
- W2802121752 created "2018-05-17" @default.
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- W2802121752 date "2018-05-07" @default.
- W2802121752 modified "2023-09-27" @default.
- W2802121752 title "Rigidity of nonnegatively curved surfaces relative to a curve" @default.
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