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arXiv · 2507.18496

Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$

Flávio Cruz·José T. Cruz·Jocel Oliveira
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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.

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Flávio Cruz, José T. Cruz, Jocel Oliveira. 2025-07-24. Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$. https://arxiv.org/abs/2507.18496

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