Tohoku Mathematical Journal
2006
September
SECOND SERIES VOL. 58, NO. 3

Tohoku Math. J.
58 (2006), 359-368

Title A NON-EXISTENCE THEOREM OF PROPER HARMONIC MORPHISMS FROM WEAKLY ASYMPTOTICALLY HYPERBOLIC MANIFOLDS

Author Xiaohuan Mo and Yuguang Shi

(Received September 30, 2004, revised May 6, 2005)
Abstract. We prove a non-existence theorem for proper harmonic morphisms from weakly asymptotically hyperbolic manifolds to hyperbolic manifolds which are $C^2$ up to the boundary at infinity.

2000 Mathematics Subject Classification. Primary 53C55; Secondary 58E20.
Key words and phrases. Harmonic morphism, weakly asymptotically hyperbolic manifold, conformally compact manifold, proper map, harmonic map.

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