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• W1973452010 abstract "We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as well as expanding soltions with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with lower bounds characterized by the geometry of the manifold. The geometric invariant appearing in the sharp lower bound is shown to be nonnegative. We also characterize the expanders when such invariant is zero. In the proof various useful volume growth estimates are also established for gradient shrinking and expanding solitons. In particular, we prove that the {it asymptotic volume ratio} of any gradient shrinking soliton with nonnegative Ricci curvature must be zero." @default.
• W1973452010 created "2016-06-24" @default.
• W1973452010 creator A5054419282 @default.
• W1973452010 creator A5080131819 @default.
• W1973452010 date "2008-06-15" @default.
• W1973452010 modified "2023-09-27" @default.
• W1973452010 title "Sharp logarithmic Sobolev inequalities on gradient solitons and applications" @default.
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