Calculus of Variations and Geometric Measure Theory

M. Perugini

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

created by perugini on 30 Nov 2023
modified on 05 Jan 2024


Published Paper

Inserted: 30 nov 2023
Last Updated: 5 jan 2024

Journal: Nonlinear Analysis
Pages: 22
Year: 2023

ArXiv: 2311.17818 PDF


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.

Keywords: Steiner symmetrisation, circular symmetrisation