Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
- Cite this article as:
- Wang, FY. 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.