Rigidity phenomenons for an infinite dimension diffusion operator and\n cases of near equality in the Bakry--Ledoux isoperimetric comparison Theorem

2017/08/23 by Raphaël Bouyrie, Bouyrie, Raphael
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1708.07203

openalex publication_date 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study rigidity phenomenons for infinite dimension diffusion operators of\npositive curvature using semigroup interpolations. In particular, for such\ndiffusions, an analogous statement of Obata's theorem is established. Moreover,\nthe same rigidity holds for the Bakry--Ledoux isoperimetric comparison Theorem\n- a result due to Franck Morgan. Recently, Mossel and Neeman have exploited the\nsemigroup proof of Bakry and Ledoux to derive dimension free bounds for the\nGaussian isoperimetry. We extend theirs arguments to obtain in particular new\nquantitative bounds on the spherical isoperimetric inequality in large\ndimension.\n

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