English

A new proof of a characterization of small spherical caps

Differential Geometry 2009-06-19 v1

Abstract

It is known that planar disks and small spherical caps are the only constant mean curvature graphs whose boundary is a round circle. Usually, the proof invokes the Maximum Principle for elliptic equations. This paper presents a new proof of this result motivated by an article due to Reilly. Our proof utilizes a flux formula for surfaces with constant mean curvature together with integral equalities on the surface.

Keywords

Cite

@article{arxiv.0906.3298,
  title  = {A new proof of a characterization of small spherical caps},
  author = {Rafael López},
  journal= {arXiv preprint arXiv:0906.3298},
  year   = {2009}
}

Comments

11 pages. to appear in Results in Mathematics