Given $ n \geq 2 $ and $ k \in \{2, \ldots , n\} $, we study the asymptotic behaviour of sequences of bounded $C<^>{2}$-domains, whose $ k $-th mean curvature functions converge in $ L<^>{1} $-norm to a constant. Under certain curvature assumptions, we prove that finite unions of mutually tangent balls are the only possible limits with respect to convergence in volume and perimeter. The key novelty of our statement lies in the fact that we do not assume bounds on the exterior or interior touching balls.

Finite Total Curvature and Soap Bubbles With Almost Constant Higher-Order Mean Curvature

Santilli, Mario
2024-01-01

Abstract

Given $ n \geq 2 $ and $ k \in \{2, \ldots , n\} $, we study the asymptotic behaviour of sequences of bounded $C<^>{2}$-domains, whose $ k $-th mean curvature functions converge in $ L<^>{1} $-norm to a constant. Under certain curvature assumptions, we prove that finite unions of mutually tangent balls are the only possible limits with respect to convergence in volume and perimeter. The key novelty of our statement lies in the fact that we do not assume bounds on the exterior or interior touching balls.
File in questo prodotto:
File Dimensione Formato  
Final.pdf

solo utenti autorizzati

Tipologia: Documento in Versione Editoriale
Licenza: Copyright dell'editore
Dimensione 874.95 kB
Formato Adobe PDF
874.95 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/11697/245059
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact