Mathematical Research Letters

Volume 8, Issue 6, November 2001 pp. 801-812.

Harmonic maps and the topology of conformally compact Einstein manifolds

Authors: Naichung C. Leung and Tom Y. H. Wan
Author institution: University of Minnesota, Minneapolis, and The Chinese University of Hong Kong

Summary: We study the topology of a complete asymptotically hyperbolic Einstein manifold of which its conformal boundary has positive Yamabe invariant. We prove that all maps from such manifold into any nonpositively curved manifold are homotopically trivial. Our proof is based on a Bochner type argument on harmonic maps.

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