ROUGH ISOMETRY AND HARNACK INEQUALITY

  • Park, Hyeong-In ;
  • Lee, Yong-Hah
  • Published : 1996.05.01

Abstract

Certain analytic behavior of geometric objects defined on a Riemannian manifold depends on some very crude properties of the manifold. Some of those crude invariants are the volume growth rate, isoperimetric constants, and the likes. However, these crude invariants sometimes exercise surprising control over the analytic behavior.

Keywords

rough isometry;Harnack inequality;Liouville theorem;harmonic function