Tomas–Stein Restriction Estimates on Convex Cocompact Hyperbolic Manifolds

Abstract

Abstract In this paper, we investigate the Tomas–Stein restriction estimates on convex cocompact hyperbolic manifolds $\Gamma \backslash{\mathbb{H}}^{n+1}$. Via the spectral measure of the Laplacian, we prove that the Tomas–Stein restriction estimate holds when the limit set has Hausdorff dimension $\delta _\Gamma <n/2$. This provides an example for which restriction estimate holds in the presence of hyperbolic geodesic trapping.