A surface with discontinuous isoperimetric profile
Panos Papasoglu, Eric Swenson
TL;DR
This paper constructs a specific 2D Riemannian manifold demonstrating that the isoperimetric profile can be discontinuous, which was previously an open question.
Contribution
It provides the first example of a complete connected 2D Riemannian manifold with a discontinuous isoperimetric profile.
Findings
Existence of a 2D manifold with discontinuous isoperimetric profile
Answers an open question by Nardulli and Pansu
Advances understanding of geometric properties of Riemannian manifolds
Abstract
We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry · Material Science and Thermodynamics · Elasticity and Wave Propagation