Constant mean curvature Radial graphs over domains of \mathbbSⁿ

2025/07/24 by Cruz, Flávio, Cruz, José T., Oliveira, Jocel
#35J60 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.18496

Abstract

We establish the existence of hypersurfaces with constant mean curvature and a prescribed boundary in Euclidean space, represented as radial graphs over domains of the unit sphere. Under the assumptions that the mean curvature of the domain's boundary is positive and that a subsolution exists for the associated Dirichlet problem, we extend Serrin's classical result to include the case of positive constant mean curvature.

Citations

• Conformal Killing graphs with prescribed mean curvature
• Regularity of the distance function to the boundary

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