Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method
Abstract
In this paper, we employ the ABP method developed by Brendle to establish the optimal Lp logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as a sharp L2 logarithmic Sobolev inequality for submanifolds in manifolds with nonnegative sectional curvature. The sharp constants in both inequalities depend on the asymptotic volume ratio of the ambient manifold.
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