Sharp logarithmic Sobolev inequalities on gradient solitons and applications
Sharp logarithmic Sobolev inequalities on gradient solitons and applications
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 solitons with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with lower bounds characterized by the geometry of the manifold.The …