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arXiv · 1912.12251

Sharp resolvent estimates on non-positively curved asymptotically hyperbolic manifolds

Yiran Wang
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Abstract

We study the high energy estimate for the resolvent $R(λ)$ of the Laplacian on non-trapping asymptotically hyperbolic manifolds (AHM). In the literature, polynomial bound of the form $\|R(λ)\| = O(|λ|^{N})$ for $|λ|$ large and $λ\in \mathbb{C}$ in strips where $R(λ)$ is holomorphic was established for some $N > -1$. We prove the optimal bound $O(|λ|^{-1})$ under the non-positive sectional curvature assumption by taking into account the oscillatory behavior of the Schwartz kernel of the resolvent.

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Yiran Wang. 2019-12-27. Sharp resolvent estimates on non-positively curved asymptotically hyperbolic manifolds. https://arxiv.org/abs/1912.12251

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