Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametrix for wave equations on a rough background III: space-time
  regularity of the phase   This is the third of a sequence of four papers \cite{param1}, \cite{param2},
\cite{param3}, \cite{param4} dedicated to the construction and the control of a
parametrix to the homogeneous wave equation $\square_{\bf g} \phi=0$, where
${\bf g}$ is a rough metric satisfying the Einstein vacuum equations.
Controlling such a parametrix as well as its error term when one only assumes
$L^2$ bounds on the curvature tensor ${\bf R}$ of ${\bf g}$ is a major step of
the proof of the bounded $L^2$ curvature conjecture proposed in \cite{Kl:2000},
and solved by S. Klainerman, I. Rodnianski and the author in \cite{boundedl2}.
On a more general level, this sequence of papers deals with the control of the
eikonal equation on a rough background, and with the derivation of $L^2$ bounds
for Fourier integral operators on manifolds with rough phases and symbols, and
as such is also of independent interest.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph