Integral Equations and Operator Theory

, Volume 48, Issue 4, pp 547–552

Equivalence of Dimension-Free Harnack Inequality and Curvature Condition

Original paper

DOI: 10.1007/s00020-002-1264-y

Cite this article as:
Wang, FY. Integr. equ. oper. theory (2004) 48: 547. doi:10.1007/s00020-002-1264-y


Some properties of a diffusion semigroup are proved to be equivalent to the curvature lower bound condition of its generator. In particular, the dimension-free Harnack inequality established in [1] holds if and only if the curvature is bounded below.

Mathematics Subject Classification (2000).

Primary: 47D07Secondary: 60H10


Curvaturediffusion semigroupHarnack inequality

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Normal UniversityBeijingChina