Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy, minimal surfaces, and negatively curved manifolds   In 2004, Taubes introduced the space of minimal hyperbolic germs with
elements consisting of the first and second fundamental form of an equivariant
immersed minimal disk in hyperbolic 3-space. Herein, we initiate a further
study of this space by studying the behavior of a dynamically defined function
which records the entropy of the geodesic flow on the associated Riemannian
surface. We provide a useful estimate on this function which, in particular,
yields a new proof of Bowen's theorem on the rigidity of the Hausdorff
dimension of the limit set of quasi-Fuchsian groups. These follow from new
lower bounds on the Hausdorff dimension of the limit set which allow us to give
a quantitative version of Bowen's rigidity theorem. To demonstrate the strength
of the techniques, these results are generalized to convex-cocompact surface
groups acting on $n$-dimensional CAT$(-1)$ Riemannian manifolds.

10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph