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Stationary surfaces for the moment of inertia with constant Gauss curvature

  • Rafael López ORCID logo EMAIL logo
Published/Copyright: September 17, 2025
Analysis
From the journal Analysis

Abstract

Consider the energy E α [ Σ ] = Σ | p | α d Σ , where Σ is a surface in Euclidean space R 3 and α 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.

MSC 2020: 53A10; 49Q05; 35A15

Award Identifier / Grant number: PID2023-150727NB-I00

Award Identifier / Grant number: CEX2020-001105-M

Funding statement: 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.

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Received: 2025-04-29
Accepted: 2025-08-30
Published Online: 2025-09-17

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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