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arXiv · 2310.08005

Uniqueness of blowups for forced mean curvature flow

Sven Hirsch·Jonathan J. Zhu
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Abstract

We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by Schulze and Colding-Minicozzi respectively. We adapt their methods to handle the presence of the forcing term, which vanishes in the blow-up limit but complicates the analysis along the rescaled flow. Our results naturally include the case of mean curvature flows in Riemannian manifolds.

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Sven Hirsch, Jonathan J. Zhu. 2023-10-12. Uniqueness of blowups for forced mean curvature flow. https://arxiv.org/abs/2310.08005

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