Title: Trace formula for billiard flow on surfaces with concave boundary
Abstract: We study grazing closed trajectories of the billiard flow $\varphi^t$ on a compact surface $(\Sigma,g)$ with concave boundary. Under a non-degeneracy condition, which is satisfied for example when $(\Sigma,g)$ has negative sectional curvature, we compute the trace of a regularized pullback $E_{\epsilon}(\varphi^t)^* E_{\epsilon}$ near a closed trajectory grazing once, which is an analogue of the Atiyah--Bott--Guillemin trace formula for closed billiard trajectories.
Jared Wunsch
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