Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improvement of eigenfunction estimates on manifolds of nonpositive
  curvature   Let $(M,g)$ be a compact, boundaryless manifold of dimension $n$ with the
property that either (i) $n=2$ and $(M,g)$ has no conjugate points, or (ii) the
sectional curvatures of $(M,g)$ are nonpositive. Let $\Delta$ be the positive
Laplacian on $M$ determined by $g$. We study the $L^{2}\to{}L^{p}$ mapping
properties of a spectral cluster of $\sqrt{\Delta}$ of width $1/\log\lambda$.
Under the geometric assumptions above, \cite{berard77} B\'{e}rard obtained a
logarithmic improvement for the remainder term of the eigenvalue counting
function which directly leads to a $(\log\lambda)^{1/2}$ improvement for
H\"ormander's estimate on the $L^{\infty}$ norms of eigenfunctions. In this
paper we extend this improvement to the $L^p$ estimates for all
$p>\frac{2(n+1)}{n-1}$.

0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat