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.
Perimeter inequality; cases of equality; Steiner symmetrisation; circular symmetrisation;
Settore MAT/05 - Analisi Matematica
1-mar-2024
http://arxiv.org/abs/2311.17818v1
Article (author)
File in questo prodotto:
File Dimensione Formato  
2311.17818.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 449.95 kB
Formato Adobe PDF
449.95 kB Adobe PDF Visualizza/Apri
1-s2.0-S0362546X23002523-main.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 708.7 kB
Formato Adobe PDF
708.7 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1019854
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
  • OpenAlex ND
social impact