DOI QR코드

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ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS AND EXPONENTIALLY HARMONIC FUNCTIONS

  • Chi, Dong-Pyo (Department of Mathematics Seoul National University Seoul 151-742) ;
  • Choi, Gun-Don (School of Computer Science and Engineering Seoul National University Seoul 151-742) ;
  • Chang, Jeong-Wook (Department of Mathematics Korea Advanced Institute of Science and Technology Taejon, 305-701)
  • Published : 2002.09.01

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

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