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.
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