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Integral formulas for the Laplacian along the unstable foliation and applications to rigidity problems for manifolds of negative curvature

Published online by Cambridge University Press:  19 September 2008

Chengbo Yue
Chengbo Yue
Affiliation:
Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley CA 94720, USA
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Abstract

We obtain a class of integral formulas for the Lapacian along unstable leaves of the geodesic flow of compact manifolds of negative curvature. Using these formulas, we give two functional descriptions of those manifolds with horospheres having constant mean curvature. More rigidity problems are discussed, including a simple proof of two important Lemmas by Hamenstadt which avoids her use of stochastic process.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 803 - 819
Copyright
Copyright © Cambridge University Press 1991

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