Stable capillary hypersurfaces and the partitioning problem in balls with radial weights Rosales Lombardo, Manuel César Weighted manifolds Radial weights Capillary hypersurfaces Partitioning problem Stability In a round ball B ⊂ Rn+1 endowed with an O(n+1)-invariant metric we consider a radial function that weights volume and area. We prove that a compact two-sided hypersurface in B which is stable capillary in weighted sense and symmetric about some line containing the center of B is homeomorphic to a closed n-dimensional disk. When combined with Hsiang symmetrization and other stability results this allows to deduce that the interior boundary of any isoperimetric region in B for the Gaussian weight is a closed n-disk of revolution. For n = 2 we also show that a compact weighted stable capillary surface in B of genus 0 is a closed disk of revolution. 2023-07-25T11:06:02Z 2023-07-25T11:06:02Z 2023-04-09 journal article C. Rosales. Stable capillary hypersurfaces and the partitioning problem in balls with radial weights. Nonlinear Analysis 233 (2023) 113291[https://doi.org/10.1016/j.na.2023.113291] https://hdl.handle.net/10481/83978 10.1016/j.na.2023.113291 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier