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Harmonic maps and the topology of conformally compact Einstein manifolds

Naichung Conan Leung·Tom Yau-heng Wan
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Abstract

We study the topology of a complete asymptotically hyperbolic Einstein manifold such that its conformal boundary has positive Yamabe invariant. We proved 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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Naichung Conan Leung, Tom Yau-heng Wan. 2001-12-03. Harmonic maps and the topology of conformally compact Einstein manifolds. https://arxiv.org/abs/math/0112023

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