Another billiard problem

Sergey Bolotin, Dmitry Treschev

Let $(M,g)$ be a Riemannian manifold, $\hat{I}\text{c◯}\subset M$ a domain with boundary $\hat{I}“$, and $\ddot{I}•$ a smooth function such that $\ddot{I}•{|}_{\hat{I}}\text{c◯}>0$, $\ph|_Γ= 0$, and $\nabla \ddot{I}•{|}_{\hat{I}}“\ne 0$. We study t…