A discontinuous isoperimetric profile for a complete Riemannian manifold

Abstract

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

References in corpus (3)

• Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions
• Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume

Cited by in corpus (5)

• Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions
• Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume
• Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow
• The Optimal Double Bubble for Density $r^p$