Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems

Abstract

We study the isoperimetric problem in the Riemannian products S 1 (r) Q n c , where Q n c is the n-dimensional simply connected space form of constant sectional curvature c = 0, 1, -1, and r > 0. The problem of classifying stable free boundary hypersurfaces with constant mean curvature between two parallel hyperplanes in R n for n 3 is also treated.