Anisotropic perimeter and isoperimetric quotient of inner parallel bodies

2021/01/09 by Graziano Crasta, Crasta, Graziano
Mathematics · #52A20 #52A38 #52A39 #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Metric Geometry (math.MG) #Point processes and geometric inequalities #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2101.03307

openalex publication_date 2021/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this note is twofold: to give a short proof of the results in [S. Larson, A bound for the perimeter of inner parallel bodies, J. Funct. Anal. 271 (2016), 610-619] and [G. Domokos and Z. Lángi, The isoperimetric quotient of a convex body decreases monotonically under the eikonal abrasion model, Mathematika 65 (2019), 119-129]; and to generalize them to the anisotropic case.

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