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arXiv · 2605.21193

Sharp Gaussian Isoperimetry along a Ricci Flow

Robert Koirala
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Abstract

We prove the sharp Gaussian isoperimetric inequality for conjugate heat-kernel measures along a Ricci flow via a monotonicity formula. As consequences, we obtain the exact Gaussian enlargement theorem and a Gaussian-quantile two-set concentration estimate. In particular, this recovers the exponential concentration estimate of Hein--Naber from a sharper isoperimetric profile. We also derive Gaussian rearrangement inequalities, recover the sharp Hein--Naber log-Sobolev inequality, and identify the universal Gaussian-model constants in Bamler's \(L^p\)-Poincar\'e inequalities. Further applications include Gaussian-profile localization near Bamler's \(H_n\)-centers, convex-order and moment estimates for logarithmic derivatives of the conjugate heat kernel, reverse hypercontractivity, entropy-regular profile stability, and a path-space Bobkov inequality.

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Robert Koirala. 2026-05-20. Sharp Gaussian Isoperimetry along a Ricci Flow. https://arxiv.org/abs/2605.21193

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