A new proof of a characterization of small spherical caps
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Publication:844026
DOI10.1007/S00025-009-0412-YzbMATH Open1180.53010arXiv0906.3298OpenAlexW2593983098MaRDI QIDQ844026
Publication date: 18 January 2010
Published in: Results in Mathematics (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/0906.3298
Related Items (4)
A new construction of caps ⋮ Asymptotic values of minimal graphs in a disc ⋮ Families of spherical caps: spectra and ray limit ⋮ Characterizations of balls by sections and caps
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