Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shrinking doughnuts via variational methods   We use variational methods and a modified curvature flow to give an
alternative proof of the existence of a self-shrinking torus under mean
curvature flow. As a consequence of the proof, we establish an upper bound for
the weighted energy of our shrinking doughnuts.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn