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arXiv · 2007.03928

Non-parametric mean curvature flow with prescribed contact angle in Riemannian products

Jean-Baptiste Casteras·Esko Heinonen·Ilkka Holopainen·Jorge H. de Lira
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Abstract

Assuming that there exists a translating soliton $u_\infty$ with speed $C$ in a domain $\Omega$ and with prescribed contact angle on $\partial\Omega$, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to $u_\infty +Ct$ as $t\to\infty$. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of $\Omega$ and Ricci curvature in $\Omega$.

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Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen, Jorge H. de Lira. 2020-07-08. Non-parametric mean curvature flow with prescribed contact angle in Riemannian products. https://doi.org/10.1515/agms-2020-0132

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