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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A new proof of the rigidity problem

Author: Chang-Wan Kim
Journal: Proc. Amer. Math. Soc. 136 (2008), 3635-3638
MSC (2000): Primary 53C20, 53C60
Published electronically: May 22, 2008
MathSciNet review: 2415048
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Abstract: In this short note we give a new proof of the boundary rigidity problem in a Euclidean setting proved by Croke. Our method is based on the differentiability of Busemann functions and the characteristic of Euclidean metric on Riemannian manifolds without conjugate points.

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Chang-Wan Kim
Affiliation: Korea Institute for Advanced Study, 207-43 CheongNyangNi 2-Dong, DongDaeMun-Gu Seoul 130-722, Republic of Korea

Keywords: Boundary rigid, Busemann functions, Santal\'{o}'s formula
Received by editor(s): September 18, 2006
Published electronically: May 22, 2008
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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