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.
Perimeter inequality under circular and Steiner symmetrisation: geometric characterisation of extremals / M. Perugini. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 240:(2024 Mar 01), pp. 113460.1-113460.19. [10.1016/j.na.2023.11346]
Perimeter inequality under circular and Steiner symmetrisation: geometric characterisation of extremals
M. Perugini
2024
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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