Two classification results for stationary surfaces of the least moment of inertia López Camino, Rafael Stationary surfaces Moment of inertia Ruled surface 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. A surface in Euclidean space R3 is said to be an α-stationary surface if it is a critical point of the energy ∫Σ|p|α, where α∈R. These surfaces are characterized by the Euler-Lagrange equation H(p)=α⟨N(p),p⟩|p|2, p∈Σ, where H and N are the mean curvature and the normal vector of Σ. If α≠0, we prove that vector planes are the only ruled α-stationary surfaces. The second result of classification asserts that if α≠−2,−4, any α-stationary surface foliated by circles must be a surface of revolution. If α=−4, the surface is the inversion of a plane, a helicoid, a catenoid or an Riemann minimal example. If α=−2, and besides spheres centered at 0, we find non-spherical cyclic −-stationary surfaces. 2026-01-22T10:31:04Z 2026-01-22T10:31:04Z 2025 journal article López Camino, Rafael. Two classification results for stationary surfaces of the least moment of inertia. International Electronic Journal of Geometry, 18 (2) (2025), 425-436. https://hdl.handle.net/10481/110084 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License