Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An example of $\alpha$-harmonic map sequence for which energy identity
  is not true   We construct a closed Riemannian manifold $(N,h)$ and a sequence of
$\alpha$-harmonic maps from $S^2$ into $N$ with uniformly bounded energy such
that the energy identity for this sequence is not true.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg