Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Sharp Lower Bound for the Entropy of Closed Hypersurfaces up to
  Dimension Six   In [5], Colding-Ilmanen-Minicozzi-White showed that within the class of
closed smooth self-shrinkers in $\mathbb{R}^{n+1}$, the entropy is uniquely
minimized at the round sphere. They conjectured that, for $2\leq n\leq 6$, the
round sphere minimizes the entropy among all closed smooth hypersurfaces. Using
an appropriate weak mean curvature flow, we prove their conjecture. For these
dimensions, our approach also gives a new proof of the main result of [5] and
extends its conclusions to compact singular self-shrinkers.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas