Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mappings of finite distortion: compactness of the branch set   We show that an entire branched cover of finite distortion cannot have a
compact branch set if its distortion satisfies a certain asymptotic growth
condition. We furthermore show that this bound is strict by constructing an
entire, continuous, open and discrete mapping of finite distortion which is
piecewise smooth, has a branch set homeomorphic to $(n-2)$-dimensional torus
and distortion arbitrarily close to the asymptotic bound.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas