Mathematical Research Letters
Volume 8 (2001)
Harmonic maps and the topology of conformally compact Einstein manifolds
Pages: 801 – 812
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.