Plateau-Rayleigh instability of singular minimal surfaces López Camino, Rafael We prove a Plateau-Rayleigh criterion of instability for singular minimal surfaces, providing explicit bounds on the amplitude and length of the surface. More generally, we study the stability of α-singular minimal hypersurfaces considered as hypersurfaces in weighted manifolds. If α < 0 and the hypersurface is a graph, then we prove that the hypersurface is stable. If α > 0 and the surface is cylindrical, we give numerical evidences of the instability of long cylindrical α-singular minimal surfaces. 2026-01-21T12:43:41Z 2026-01-21T12:43:41Z 2022 journal article Publisher version: López Camino, R. (2022). Plateau-Rayleigh instability of singular minimal surfaces. Communications on Pure and Applied Analysis, vol. 21, no. 9, 2981-2997, Doi: 10.3934/cpaa.2022086 https://hdl.handle.net/10481/110048 10.3934/cpaa.2022086 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License American Institute of Mathematical Sciences