Geometric stability of the Coulomb energy
Almut Burchard, Gregory R. Chambers
TL;DR
This paper demonstrates that sets with Coulomb energy close to the maximum are geometrically close to spherical shapes, establishing stability of the Coulomb energy maximization problem.
Contribution
It proves the geometric stability of Coulomb energy maximizers, showing near-maximizers are close to balls in shape.
Findings
Near-maximizers of Coulomb energy are close to spherical shapes.
Maximizers of Coulomb energy are balls.
Stability result quantifies how close near-maximizers are to balls.
Abstract
The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.
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.