Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On H\"older regularity of the singular set of energy minimizing harmonic
  maps into closed manifolds   Energy minimizing harmonic maps between manifolds are known to be smooth
outside a rectifiable set of codimension $3$, called the singular set. The
possibility that this set is not a manifold, but has arbitrarily many small
gaps in it, is not excluded in general. Here we prove that some part of the
singular set - characterized by topological and analytic properties of tangent
maps - is a topological manifold. In the special case of maps into the sphere
${\mathbb S}^2$, we conclude that the whole top-dimensional part of the
singular set is a manifold - this generalizes a similar result in
two-dimensional domain, due to Hardt and Lin.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom