Quantitative estimates for the Bakry-Ledoux isoperimetric inequality. II

Abstract

Concerning quantitative isoperimetry for a weighted Riemannian manifold satisfying ${\mathrm{Ric}}_{\infty }\ge 1$, we give an $L^1$-estimate exhibiting that the push-forward of the reference measure by the guiding function (arising from the needle decomposition) is close to the Gaussian measure. We also show $L^p$- and $W_2$-estimates in the $1$-dimensional case.

v2: 10 pages, to appear in Bull. Lond. Math. Soc

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