Probability Theory and Related Fields

, Volume 109, Issue 3, pp 417–424

Logarithmic Sobolev inequalities on noncompact Riemannian manifolds


  • Feng-Yu Wang
    • Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China e-mail:

DOI: 10.1007/s004400050137

Cite this article as:
Wang, F. Probab Theory Relat Fields (1997) 109: 417. doi:10.1007/s004400050137


This paper presents a dimension-free Harnack type inequality for heat semigroups on manifolds, from which a dimension-free lower bound is obtained for the logarithmic Sobolev constant on compact manifolds and a new criterion is proved for the logarithmic Sobolev inequalities (abbrev. LSI) on noncompact manifolds. As a result, it is shown that LSI may hold even though the curvature of the operator is negative everywhere.

AMS Subject Classification (1991): 35P1560J60

Copyright information

© Springer-Verlag Berlin Heidelberg 1997