More on functional and quantitative versions of the isoperimetric inequality

2016/09/14 by Erik G. F. Thomas, Thomas, Erik
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Inequalities and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1609.04179

openalex publication_date 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein distance of the classical isopemetric inequality. In both parts, we use optimal transportation. Finally, we use our refined isoperimetric inequality in some classical cases arising in convex geometry.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions

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