Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every conformal class contains a metric of bounded geometry   We show that on every manifold, every conformal class of semi-Riemannian
metrics contains a metric $g$ such that each $k$-th-order covariant derivative
of the Riemann tensor of $g$ has bounded absolute value $a_k$. This result is
new also in the Riemannian case, where one can arrange in addition that $g$ is
complete with injectivity and convexity radius greater than 1. One can even
make the radii rapidly increasing and the functions $a_k$ rapidly decreasing at
infinity. We prove generalizations to foliated manifolds, where curvature,
second fundamental form and injectivity radius of the leaves can be controlled
similarly. Moreover, we explain a general principle that can be used to obtain
analogous results for Riemannian manifolds equipped with arbitrary other
additional geometric structures instead of foliations.

27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org