Isoperimetric Regions in Nonpositively Curved Manifolds

Abstract

Isoperimetric regions minimize the size of their boundaries among all regions with the same volume. In Euclidean and Hyperbolic space, isoperimetric regions are round balls. We show that isoperimetric regions in two and three-dimensional nonpositively curved manifolds are not necessarily balls, and need not even be connected.

Cited by in corpus (2)

• Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions
• Asymptotic dimension of planes and planar graphs