Isoperimetric inequalities in cylinders with density. (April 2022) - Castro, Katherine
Abstract: Given a compact Riemannian manifold with density M without boundary and the real line R with constant density, we prove that isoperimetric regions of large volume in M × R with the product density are slabs of the form M × [ a, b ] . We previously prove, as a necessary step, the existence of isoperimetric regions in any manifold of density where a subgroup of the group of transformations preserving weighted perimeter and volume acts cocompactly.