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March 14, 2026Nonlinear Analysis0 citationsOpen Access

Constant mean curvature radial graphs over domains of S n

FCFlávio CruzUniversidade Federal do Cariri JCJosé Tiago Nogueira CruzUniversidade Federal do Cariri JOJocel Faustino Norberto de OliveiraUniversidade Federal do Cariri

Key Points

The study aims to show the existence of hypersurfaces with constant mean curvature and a specific boundary in Euclidean space.
Analysis of radial graphs over domains of the unit sphere
Conditions of positive mean curvature on domain boundaries
Application of Serrin’s result to this extended case
Existence of hypersurfaces with constant mean curvature confirmed
Extension of classical results to include positive constant mean curvature
Conditions set for boundaries and subsolutions are satisfied

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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Cite This Study

Cruz et al. (Wed,) studied this question.

synapsesocial.com/papers/69b4fb1bb39f7826a300bb28 https://doi.org/https://doi.org/10.1016/j.na.2026.114097

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