Wang, Feng-Yu Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. (English) Zbl 0887.35012 Probab. Theory Relat. Fields 109, No. 3, 417-424 (1997). Summary: 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 (LSI) on noncompact manifolds. As a result, it is shown that LSI may hold even though the curvature of the operator is negative everywhere. Cited in 8 ReviewsCited in 133 Documents MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 26D10 Inequalities involving derivatives and differential and integral operators 60J60 Diffusion processes Keywords:Harnack type inequality; heat semigroups on manifolds PDFBibTeX XMLCite \textit{F.-Y. Wang}, Probab. Theory Relat. Fields 109, No. 3, 417--424 (1997; Zbl 0887.35012) Full Text: DOI