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 (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.
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Received: 24 July 1996 / In revised form: 25 June 1997
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Wang, FY. Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Probab Theory Relat Fields 109, 417–424 (1997). https://doi.org/10.1007/s004400050137
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DOI: https://doi.org/10.1007/s004400050137