Mathematical Research Letters

Volume 8 (2001)

Number 6

Harmonic maps and the topology of conformally compact Einstein manifolds

Pages: 801 – 812



Naichung C. Leung (University of Minnesota, Minneapolis)

Tom Y. H. Wan (The Chinese University of Hong Kong)


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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