Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Sobolev Estimates on compact manifolds involving singular
  potentials   We obtain generalizations of the uniform Sobolev inequalities of Kenig, Ruiz
and the fourth author \cite{KRS} for Euclidean spaces and Dos Santos Ferreira,
Kenig and Salo \cite{DKS} for compact Riemannian manifolds involving critically
singular potentials $V\in L^{n/2}$. We also obtain the analogous improved
quasimode estimates of the the first, third and fourth authors \cite{BSS} ,
Hassell and Tacy \cite{HassellTacy}, the first and fourth author \cite{SBLog},
and Hickman \cite{Hickman} as well as analogues of the improved uniform Sobolev
estimates of \cite{BSSY} and \cite{Hickman} involving such potentials.
Additionally, on $S^n$, we obtain sharp uniform Sobolev inequalities involving
such potentials for the optimal range of exponents, which extend the results of
S. Huang and the fourth author \cite{SHSo}. For general Riemannian manifolds we
improve the earlier results in \cite{BSS} by obtaining quasimode estimates for
a larger (and optimal) range of exponents under the weaker assumption that
$V\in L^{n/2}$.

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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: stat