Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. (English) Zbl 0887.35012

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.


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
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