A new proof of the rigidity problem

Kim, Chang-Wan

doi:10.1090/S0002-9939-08-09082-5

A new proof of the rigidity problem
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Proc. Amer. Math. Soc. 136 (2008), 3635-3638 Request permission

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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