English

Prescribed mean curvature equation on torus

Analysis of PDEs 2020-11-12 v1 Differential Geometry

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 nn-dimensional torus Tn\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.

Keywords

Cite

@article{arxiv.2011.05469,
  title  = {Prescribed mean curvature equation on torus},
  author = {Yuki Tsukamoto},
  journal= {arXiv preprint arXiv:2011.05469},
  year   = {2020}
}

Comments

11 pages

R2 v1 2026-06-23T20:03:58.648Z