Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions

Abstract

Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatures.

Final version. One reference added

References in corpus (4)

• Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• A discontinuous isoperimetric profile for a complete Riemannian manifold
• Some isoperimetric comparison theorems for convex bodies in Riemannian manifolds
• Isoperimetric Regions in Nonpositively Curved Manifolds

Cited by in corpus (10)

• On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
• Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• A discontinuous isoperimetric profile for a complete Riemannian manifold
• Existence of Self-Cheeger sets on Riemannian manifolds
• A reciprocity principle for constrained isoperimetric problems and existence of isoperimetric subregions in convex sets
• Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow
• A surface with discontinuous isoperimetric profile
• Constant Mean Curvature Surfaces in Homology Classes
• Isoperimetric rigidity and distributions of 1-Lipschitz functions