Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Space of Weak Connections in High Dimensions   The space of Sobolev connections, as it has been introduced for studying the
variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not
to be weakly sequentially complete in dimension larger than $4$. This is a
major obstruction for studying the variations of this important Lagrangian in
high dimensions. The present paper generalizes the previous result of the
authors from 'The resolution of the Yang-Mills Plateau problem in
super-critical dimensions', Adv. Math. 316 (arxiv:1306.2010), valid in $5$
dimensions to arbitrary dimension and introduces a space of so called 'weak
connections' for which we prove the weak sequential closure under Yang-Mills
energy control. We also establish a strong approximation property of any weak
connection by smooth connections away from codimension $5$ polyhedral sets.
This last property is used in a subsequent work in preparation for establishing
the partial regularity property for general stationary Yang-Mills weak
connections.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol