We show that two properly embedded self-shrinkers in Euclidean space that are sufficiently separated at infinity must intersect at a finite point. The proof is based on a localized version of the Reilly formula applied to a suitable f-harmonic function with controlled gradient. In the immersed case, a new direct proof of the generalized half-space property is also presented.

Impera, D., Pigola, S., Rimoldi, M. (2021). The Frankel property for self-shrinkers from the viewpoint of elliptic PDEs. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 773(1 april 2021), 1-20 [10.1515/crelle-2020-0044].

The Frankel property for self-shrinkers from the viewpoint of elliptic PDEs

Pigola S.;
2021

Abstract

We show that two properly embedded self-shrinkers in Euclidean space that are sufficiently separated at infinity must intersect at a finite point. The proof is based on a localized version of the Reilly formula applied to a suitable f-harmonic function with controlled gradient. In the immersed case, a new direct proof of the generalized half-space property is also presented.
Articolo in rivista - Articolo scientifico
self-shrinkers, intersection property, half-space property;
English
15-dic-2020
2021
773
1 april 2021
1
20
open
Impera, D., Pigola, S., Rimoldi, M. (2021). The Frankel property for self-shrinkers from the viewpoint of elliptic PDEs. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 773(1 april 2021), 1-20 [10.1515/crelle-2020-0044].
File in questo prodotto:
File Dimensione Formato  
10281-300573_VoR.pdf

accesso aperto

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Licenza: Creative Commons
Dimensione 406.41 kB
Formato Adobe PDF
406.41 kB Adobe PDF Visualizza/Apri

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/10281/300573
Citazioni
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 4
Social impact