Integrable Billiards and Related Topics
arXiv:2510.03790
Abstract
This paper surveys our results on integrable billiards. We consider various models of billiards, including Birkhoff, outer, magnetic, and Minkowski billiards. Also, we discuss wire billiards and billiards in cones. For four models of convex plane billiards, we also discuss an isoperimetric-type inequality for the Mather -function. We conclude with a section of open questions on this subject.
Submitted to the proceedings of ICM 2026