A new proof of a characterization of small spherical caps

Details A new proof of a characterization of small spherical caps A new proof of a characterization of small spherical caps

2009-06-17

arxiv.org/abs/0906.3298v1

Mathematics

Differential Geometry

11 pages. to appear in Results in Mathematics

Scientific paper

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.

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