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A new proof of the rigidity problem
Author(s):
Chang-Wan
Kim
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3635-3638.
MSC (2000):
Primary 53C20, 53C60
Posted:
May 22, 2008
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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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Additional Information:
Chang-Wan
Kim
Affiliation:
Korea Institute for Advanced Study, 207-43 CheongNyangNi 2-Dong, DongDaeMun-Gu Seoul 130-722, Republic of Korea
Email:
cwkimgrf@kias.re.kr
DOI:
10.1090/S0002-9939-08-09082-5
PII:
S 0002-9939(08)09082-5
Keywords:
Boundary rigid,
Busemann functions,
Santal\'{o}'s formula
Received by editor(s):
September 18, 2006
Posted:
May 22, 2008
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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