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arXiv · 2507.12865

Stationary surfaces for the moment of inertia with constant Gauss curvature

Rafael López
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Abstract

Consider the energy $E_α[Σ]=\int_Σ|p|^α\, dΣ$, where $Σ$ is a surface in Euclidean space $\r^3$ and $α\in\r$. We prove that planes and spheres are the only stationary surfaces for $E_α$ 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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Rafael López. 2025-07-17. Stationary surfaces for the moment of inertia with constant Gauss curvature. https://arxiv.org/abs/2507.12865

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