Strictly Locally Convex Hypersurfaces with Prescribed Curvature and Boundary in Space Forms

Zhenan Sui

Strictly Locally Convex Hypersurfaces with Prescribed Curvature and Boundary in Space Forms

Analysis of PDEs 2019-11-05 v2 Differential Geometry

Authors: Zhenan Sui

Abstract

This paper is devoted to $C^2$ a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature equation under the assumption of a strictly locally convex subsolution.

Keywords

locally convex hypersurfaces weingarten curvature space forms a priori estimates gauss curvature subsolution degree theory

Cite

@article{arxiv.1805.08107,
  title  = {Strictly Locally Convex Hypersurfaces with Prescribed Curvature and Boundary in Space Forms},
  author = {Zhenan Sui},
  journal= {arXiv preprint arXiv:1805.08107},
  year   = {2019}
}

Comments

30 pages, final accepted version with many updates

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