Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Rigidity of Ricci shrinkers of dimension four   In dimension $4$, we show that a nontrivial flat cone cannot be approximated
by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality,
under the pointed-Gromov-Hausdorff topology. As applications, we obtain uniform
positive lower bounds of scalar curvature and potential functions on Ricci
shrinkers satisfying some natural geometric properties.

14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an