Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ROUGH ISOMETRY, HARMONIC FUNCTIONS AND HARMONIC MAPS ON A COMPLETE RIEMANNIAN MANIFOLD

  • Kim, Seok-Woo (Department of Mathematics seoul National University) ;
  • Lee, Yong-Han (Department of Mathematics seoul National University)
  • Published : 1999.01.01
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Abstract

We prove that if a given complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincar inequality and the finite covering condition at infinity on each end, then every positive harmonic function on the manifold is asymptotically constant at infinity on each end. This result is a direct generalization of those of Yau and of Li and Tam.

Keywords

References

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