Stationary surfaces for the moment of inertia with constant Gauss curvature López Camino, Rafael Moment of inertia Stationary surfaces Gauss curvature The author has been partially supported by MINECO/MICINN/FEDER grant no. PID2023-150727NB-I00, and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105- M, funded by MCINN/AEI/10.13039/ 501100011033/CEX2020-001105-M. 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. 2026-01-22T10:23:37Z 2026-01-22T10:23:37Z 2025 journal article 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 0003-2638 1467-8284 https://hdl.handle.net/10481/110083 10.1515/anly-2025-0037 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ embargoed access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License De Gruyter