3 papers
math.SG2026
Open problems in billiards and quantitative symplectic geometry
Bernhard Albach, Jean-François Barraud, Misha Bialy +13
This document collects contributions to the Open Problem List in Billiards and Quantitative Symplectic Geometry, compiled following discussions during the workshop ``Billiards and…
math.SG2023
Hopf orbits and the first ECH capacity
Umberto Hryniewicz, Michael Hutchings, Vinicius G. B. Ramos
We consider dynamically convex star-shaped domains in a symplectic vector space of dimension . For such a domain, a ``Hopf orbit'' is a closed characteristic in the boundary whi…
math.SG2023
Proof of Hofer-Wysocki-Zehnder's two or infinity conjecture
Dan Cristofaro-Gardiner, Umberto Hryniewicz, Michael Hutchings +1
We prove that every Reeb flow on a closed connected three-manifold has either two or infinitely many simple periodic orbits, assuming that the associated contact structure has tors…