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arXiv · 2011.05469

Prescribed mean curvature equation on torus

Yuki Tsukamoto
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Abstract

Prescribed mean curvature problems on the torus has been considered in one dimension. In this paper, we prove the existence of a graph on the $n$-dimensional torus $\mathbb {T}^n$, the mean curvature vector of which equals the normal component of a given vector field satisfying suitable conditions for a Sobolev norm, the integrated value, and monotonicity.

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Yuki Tsukamoto. 2020-11-11. Prescribed mean curvature equation on torus. https://arxiv.org/abs/2011.05469

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