Contraction and regularizing properties of heat flows in metric measure\n spaces

2019/04/22 by Giulia Luise, Giuseppe Savaré, Luise, Giulia +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1904.09825

openalex publication_date 2019/04/22 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We illustrate some novel contraction and regularizing properties of the Heat\nflow in metric-measure spaces that emphasize an interplay between\nHellinger-Kakutani, Kantorovich-Wasserstein and Hellinger-Kantorvich distances.\nContraction properties of Hellinger-Kakutani distances and general Csisz 'ar\ndivergences hold in arbitrary metric-measure spaces and do not require\nassumptions on the linearity of the flow. When weaker transport distances are\ninvolved, we will show that contraction and regularizing effects rely on the\ndual formulations of the distances and are strictly related to lower Ricci\ncurvature bounds in the setting of RCD(K,\∞) metric measure spaces.\n

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