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arXiv · 1908.06584

The Dirichlet problem for a prescribed mean curvature equation

Yuki Tsukamoto
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Abstract

We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector field is sufficiently small in a dimensionally sharp Sobolev norm.

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Yuki Tsukamoto. 2019-08-19. The Dirichlet problem for a prescribed mean curvature equation. https://arxiv.org/abs/1908.06584

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