Concentration of Eigenfunctions Near a Concave Boundary

This article concerns the concentration of Dirichlet eigenfunctions of the Laplacian on a compact two-dimensional Riemannian manifold with strictly geodesically concave boundary. We link three inequalities which bound the concentration in different ways. We also prove one of these inequalities, which bounds the L ^p norms of the restrictions of eigenfunctions to broken geodesics.