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Integrable Outer billiards and rigidity by Bialy, Michael is a scholarly article available to read on EtoBox.

What is Integrable Outer billiards and rigidity about?

In the present paper we introduce a new generating function for outer billiards in the plane. Using this generating function, we prove the following rigidity result: if the vicinity of the smooth convex plane curve $\gamma$ of positive curvature is foliated by continuous curves which are invariant under outer billiard map, then the curve $\gamma$ must be an ellipse. In addition to the new generating function used in the proof, we also overcome the noncompactness of the phase space by finding suitable weights in the integral-geometric part of the proof. Thus, we reduce the result to the Blaschke-Santalo inequality.

Author

Bialy, Michael

Published

2023

Language

EN