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

Matteo Perugini

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arXiv · 2311.17818

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

Matteo Perugini

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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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Matteo Perugini. 2023-11-29. Perimeter inequality under circular and Steiner symmetrisation: geometric characterisation of extremals. https://arxiv.org/abs/2311.17818

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