A strong Frankel Theorem for shrinkers

Abstract

We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must be connected in all large balls. The key to the proof is a strong Bernstein theorem for incomplete stable Gaussian surfaces.

References in corpus (2)

• A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy
• Halfspace type Theorems for Self-Shrinkers