Two dimensional anisotropic mean curvature flow with contact angle condition

Can Cui; Nung Kwan Yip

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arXiv · 2510.22136

Two dimensional anisotropic mean curvature flow with contact angle condition

Can Cui·Nung Kwan Yip

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Abstract

In this paper, we study surfaces which evolve by anisotropic mean curvature flow with contact angle boundary condition over a strictly convex domain in $\mathbb{R}^2$. We establish a prior gradient estimate for smooth solutions to this boundary value problem. The same approach can also handle Dirichlet boundary condition in $\mathbb{R}^n$, $n\geq 2$. For both problems, we prove that the solutions converge to one that is translation invariant in time.

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Can Cui, Nung Kwan Yip. 2025-10-25. Two dimensional anisotropic mean curvature flow with contact angle condition. https://arxiv.org/abs/2510.22136

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