Singular minimal surfaces with constant curvature López Camino, Rafael Constant curvature 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. We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres, and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with constant mean curvature. 2026-01-22T10:02:27Z 2026-01-22T10:02:27Z 2025 journal article López Camino, R. (2025). Singular minimal surfaces with constant curvature. Archiv der Mathematik, 125, 659–670. https://doi.org/10.1007/s00013-025-02181-3 0003-889X 1420-8938 https://hdl.handle.net/10481/110081 10.1007/s00013-025-02181-3 http://creativecommons.org/licenses/by-nc-nd/3.0/ embargoed access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Springer Nature