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arXiv · 2509.19470

Existence of flat flows for volume-preserving mean curvature flow with contact angle

Jiwoong Jang
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Abstract

We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we establish the local-in-time equi-boundedness of approximate solutions and a uniform $L^2$-estimate of multipliers. The difficulty is handled by conducting blowup analysis at a point in contact to a spherical cap with sharp angle.

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Jiwoong Jang. 2025-09-23. Existence of flat flows for volume-preserving mean curvature flow with contact angle. https://arxiv.org/abs/2509.19470

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