Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-repulsiveness of energies for closed submanifolds   We show that the regularized Riesz $\a$-energy for closed submanifolds $M$ in
$\RR^n$ blows up as $M$ degenerates to have double points if $\a\le-2\dim M$.
This gives theoretical foundation of numerical experiments to evolve surfaces
to decrease the energy which have been carried out since 90's.

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics