Stationary surfaces for the moment of inertia with constant Gauss curvature
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Materia
Moment of inertia Stationary surfaces Gauss curvature
Date
2025Referencia bibliográfica
Publisher version: López Camino, R. (2025). Stationary surfaces for the moment of inertia with constant Gauss curvature. Analysis, vol. 45, no. 4, 259-267. https://doi.org/10.1515/anly-2025-0037
Résumé
Consider the energy Eα[Σ]=∫Σ|p|α𝑑�Σ, where Σ is a surface in Euclidean space ℝ3 and α∈ℝ. We prove that planes and spheres are the only stationary surfaces for Eα with constant Gauss curvature. We also characterize these surfaces assuming that a principal curvature is constant or that the mean curvature is constant.
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