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ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS AND EXPONENTIALLY HARMONIC FUNCTIONS
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 Title & Authors
ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS AND EXPONENTIALLY HARMONIC FUNCTIONS
Chi, Dong-Pyo; Choi, Gun-Don; Chang, Jeong-Wook;
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 Abstract
Let M be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on M. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.
 Keywords
harmonic maps;Bochner type formula;Liouville theorem;Hessian comparison theorem;
 Language
English
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