2009/06/17 by Rafael López, López, Rafael
Computer Science · Mathematics · #53A10 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG #msc:53A10
paper · pdf · doi:10.48550/arxiv.0906.3298
11 pages. to appear in Results in Mathematics
arxiv created 2009/06/17 · openalex publication_date 2009/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.