Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth Volume Rigidity for Manifolds with Negatively Curved Targets   We establish conditions for a continuous map of nonzero degree between a
smooth closed manifold and a negatively curved manifold of dimension greater
than four to be homotopic to a smooth cover, and in particular a diffeomorphism
when the degree is one. The conditions hold when the volumes or entropy-volumes
of the two manifolds differ by less than a uniform constant after an
appropriate normalization of the metrics. The results are qualitatively sharp
in the sense that the dependencies are necessary. We give a number of
corollaries.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics