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arXiv · 2601.17748

Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method

Lingen Lu
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Abstract

In this paper, we employ the ABP method developed by Brendle to establish the optimal $L^p$ logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as a sharp $L^2$ 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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Lingen Lu. 2026-01-25. Logarithmic Sobolev inequality in manifolds with nonnegative curvature via the ABP method. https://arxiv.org/abs/2601.17748

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