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A New Proof of a Characterization of Small Spherical Caps

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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.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Rafael López

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  1. Rafael López
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Correspondence to Rafael López.

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Received: July 12, 2008. Revised: June 17, 2009.

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López, R. A New Proof of a Characterization of Small Spherical Caps. Results. Math. 55, 427 (2009). https://doi.org/10.1007/s00025-009-0412-y

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  • DOI: https://doi.org/10.1007/s00025-009-0412-y

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