Another billiard problem

Sergey Bolotin, Dmitry Treschev

Let $(M,g)$ be a Riemannian manifold, $\Omega \subset M$ a domain with boundary $\Gamma$, and $\varphi$ a smooth function such that $\varphi {|}_{\Omega }>0$, $\ph|_Γ= 0$, and $\nabla \varphi {|}_{\Gamma }\ne 0$. We study the geode…