Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp resolvent estimates on non-positively curved asymptotically
  hyperbolic manifolds   We study the high energy estimate for the resolvent $R(\lambda)$ of the
Laplacian on non-trapping asymptotically hyperbolic manifolds (AHM). In the
literature, polynomial bound of the form $\|R(\lambda)\| = O(|\lambda|^{N})$
for $|\lambda|$ large and $\lambda\in \mathbb{C}$ in strips where $R(\lambda)$
is holomorphic was established for some $N > -1$. We prove the optimal bound
$O(|\lambda|^{-1})$ 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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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
20
The categories of this paper are: acc-phys