The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes

Abstract

In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are given.

33 pages, improved version after the referee comments, (Submitted)

References in corpus (3)

• Existence of isoperimetric regions in contact sub-Riemannian manifolds
• Constant mean curvature hypersurfaces condensing along a submanifold
• Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

Cited by in corpus (7)

• Existence of isoperimetric regions in contact sub-Riemannian manifolds
• The isoperimetric problem of a complete Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends
• Sharp isoperimetric inequalities for small volumes in complete noncompact Riemannian manifolds of bounded geometry involving the scalar curvature
• On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume
• Existence of Self-Cheeger sets on Riemannian manifolds
• Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity
• Eternal Forced Mean Curvature Flows II - Existence