Perimeter inequality under circular and Steiner symmetrisation: geometric characterisation of extremals

2023/11/29 by Matteo Perugini, Perugini, Matteo
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2311.17818

openalex publication_date 2023/11/29 · openalex created_date 2023/12/01 · openalex updated_date 2026/07/28

Abstract

We study the perimeter inequality under circular symmetrisation, and we provide a full geometric characterisation of equality cases. A careful inspection of the proof shows that a similar characterisation holds true also for the perimeter inequality under Steiner symmetrisation. Our result is based on a new short proof of the perimeter inequality under symmetrisation.

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