Tomas-Stein restriction estimates on convex cocompact hyperbolic manifolds. I

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.

11 pages