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arXiv · 1810.05348

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

Xiaolong Han
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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.

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Xiaolong Han. 2018-10-12. Tomas-Stein restriction estimates on convex cocompact hyperbolic manifolds. I. https://arxiv.org/abs/1810.05348

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