Boundary Regularity of Minimal Oriented Hypersurfaces on a Manifold

Simone Steinbruechel

Boundary Regularity of Minimal Oriented Hypersurfaces on a Manifold

Analysis of PDEs 2020-05-12 v1 Differential Geometry

Authors: Simone Steinbruechel

Abstract

In this article we prove that all boundary points of a minimal oriented hypersurface in a Riemannian manifold are regular, that is, in a neighborhood of any boundary point, the minimal surface is a $\mathcal{C}^{1, \frac14}$ submanifold with boundary.

Keywords

minimal hypersurface boundary regularity riemannian manifold oriented submanifold

Cite

@article{arxiv.2005.05180,
  title  = {Boundary Regularity of Minimal Oriented Hypersurfaces on a Manifold},
  author = {Simone Steinbruechel},
  journal= {arXiv preprint arXiv:2005.05180},
  year   = {2020}
}

Comments

64 pages, 10 figures

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