We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not require assumptions on the speed other than positivity and monotonicity and it is proved using a reflection argument. Our theorem shows that expanding flows exhibit stronger spherical rigidity, if compared with the classification results of ancient solutions in the contractive case.

Risa, S., Sinestrari, C. (2020). Strong spherical rigidity of ancient solutions of expansive curvature flows. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 52(2), 94-99 [10.1112/blms.12308].

Strong spherical rigidity of ancient solutions of expansive curvature flows

Risa S.;Sinestrari C.
2020-01-01

Abstract

We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not require assumptions on the speed other than positivity and monotonicity and it is proved using a reflection argument. Our theorem shows that expanding flows exhibit stronger spherical rigidity, if compared with the classification results of ancient solutions in the contractive case.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Susanna Risa has been partially supported by the group GNSAGA of INdAM (Istituto Nazionale di Alta Matematica). Carlo Sinestrari has been partially supported by the group GNAMPA of INdAM (Istituto Nazionale di Alta Matematica).
Risa, S., Sinestrari, C. (2020). Strong spherical rigidity of ancient solutions of expansive curvature flows. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 52(2), 94-99 [10.1112/blms.12308].
Risa, S; Sinestrari, C
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
16609232.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 155.38 kB
Formato Adobe PDF
155.38 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/2108/224139
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 28
  • ???jsp.display-item.citation.isi??? 7
social impact