@misc{10481/83978,
year = {2023},
month = {4},
url = {https://hdl.handle.net/10481/83978},
abstract = {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.},
publisher = {Elsevier},
keywords = {Weighted manifolds},
keywords = {Radial weights},
keywords = {Capillary hypersurfaces},
keywords = {Partitioning problem},
keywords = {Stability},
title = {Stable capillary hypersurfaces and the partitioning problem in balls with radial weights},
doi = {10.1016/j.na.2023.113291},
author = {Rosales Lombardo, Manuel César},
}