The mean curvature type hypersurfaces with prescribed gradient image

Jiguang Bao; Rongli Huang; Qinfeng Jiang

The mean curvature type hypersurfaces with prescribed gradient image

Analysis of PDEs 2026-04-22 v1

Authors: Jiguang Bao , Rongli Huang , Qinfeng Jiang

Abstract

In this paper, we consider the existence of mean curvature type hypersurfaces with prescribed gradient image. Let $\Omega$ and $\tilde{\Omega}$ be uniformly convex bounded domains in $\mathbb{R}^n$ with smooth boundary. We show that there exists unique convex solutions for the second boundary value problem of mean curvature type equations.

Keywords

hypersurfaces surfaces with constant mean curvature curvature flow

Cite

@article{arxiv.2604.19020,
  title  = {The mean curvature type hypersurfaces with prescribed gradient image},
  author = {Jiguang Bao and Rongli Huang and Qinfeng Jiang},
  journal= {arXiv preprint arXiv:2604.19020},
  year   = {2026}
}

Comments

30 pages. arXiv admin note: substantial text overlap with arXiv:2411.00817, arXiv:2404.05972

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