Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimizing 1/2-harmonic maps into spheres   In this article, we improve the partial regularity theory for minimizing
$1/2$-harmonic maps in the case where the target manifold is the
$(m-1)$-dimensional sphere. For $m\geq 3$, we show that minimizing
$1/2$-harmonic maps are smooth in dimension 2, and have a singular set of
codimension at least 3 in higher dimensions. For $m=2$, we prove that, up to an
orthogonal transformation, $x/|x|$ is the unique non trivial $0$-homogeneous
minimizing $1/2$-harmonic map from the plane into the circle $\mathbb{S}^1$. As
a corollary, each point singularity of a minimizing $1/2$-harmonic maps from a
2d domain into $\mathbb{S}^1$ has a topological charge equal to $\pm1$.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th