Rigidity of solitons of the Gauss curvature flow in Euclidean space López Camino, Rafael Gauss curvature flow Translating solitons Shrinker The author has been partially supported by MINECO/MICINN/FEDER grant no.PID2023-150727NB-I00, and by the “Mar´ıa de Maeztu” Excellence Unit IMAG, reference CEX2020-001105- M, funded by MCINN/AEI/10.13039/ 501100011033/CEX2020-001105-M. In this paper, we consider λ-translating solitons and λ-shrinkers of the Gauss curvature flow in Euclidean space. We prove that planes and circular cylinders are the only λ-translating solitons with constant mean curvature. We also prove that planes, spheres and circular cylinders are the only λ-shrinkers with constant mean curvature. We give a classification of the λ-translating solitons and λ -shrinkers with one constant principal curvature. 2026-01-22T09:52:04Z 2026-01-22T09:52:04Z 2025-06-27 journal article López Camino, R. (2025). Rigidity of solitons of the Gauss curvature flow in Euclidean space. International Journal of Mathematics, vol. 36, no. 11, 2550041. https://doi.org/10.1142/S0129167X25500417 0129-167X 1793-6519 https://hdl.handle.net/10481/110079 10.1142/S0129167X25500417 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ embargoed access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License World Scientific Publishing