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arXiv · 2507.06150

Generic mean curvature flow with obstacles

Tim Laux·Keisuke Takasao
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Abstract

We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalizes the violation of the constraint, and pass to the limit. The resulting level set formulation has unique solutions - up to fattening. Extending the work of Evans and Spruck and a work by Ullrich and one of the authors, we show that generic level sets of this flow are distributional solutions of the obstacle problem.

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Tim Laux, Keisuke Takasao. 2025-07-08. Generic mean curvature flow with obstacles. https://arxiv.org/abs/2507.06150

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