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arXiv · 1803.02332

The Frankel property for self-shrinkers from the viewpoint of elliptic PDE's

Debora Impera·Stefano Pigola·Michele Rimoldi
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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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Debora Impera, Stefano Pigola, Michele Rimoldi. 2018-03-06. The Frankel property for self-shrinkers from the viewpoint of elliptic PDE's. https://arxiv.org/abs/1803.02332

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