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The Dirichlet problem at infinity on Hadamard manifolds

Published online by Cambridge University Press:  22 January 2016

Hironori Kumura
Hironori Kumura*
Affiliation:
Department of Mathematics, Faculty of Science, Osaka University, Toyonaka, Osaka 560Japan
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Let M be an n-dimensional Hadamard manifold, that is, a complete simply connected C∞ Riemannian manifold with nonpositive sectional curvatures. Making use of geodesic rays, Eberlein and O’Neill [11] constructed a compactification = MS(∞) of M which gives a homeomorphism of (M, S(∞)) with the Euclidean pair (Bn, Sn-1). In this paper we shall study the asymptotic Dirichlet problem for the Laplace-Beltrami operator, which is stated as follows:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 138 , June 1995 , pp. 1 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

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