Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The stability inequality for Ricci-flat cones   In this article, we thoroughly investigate the stability inequality for
Ricci-flat cones. Perhaps most importantly, we prove that the Ricci-flat cone
over CP^2 is stable, showing that the first stable non-flat Ricci-flat cone
occurs in the smallest possible dimension. On the other hand, we prove that
many other examples of Ricci-flat cones over 4-manifolds are unstable, and that
Ricci-flat cones over products of Einstein manifolds and over Kahler-Einstein
manifolds with h^(1,1)>1 are unstable in dimension less than 10. As results of
independent interest, our computations indicate that the Page metric and the
Chen-LeBrun-Weber metric are unstable Ricci shrinkers. As a final bonus, we
give plenty of motivations, and partly confirm a conjecture of Tom Ilmanen
relating the lambda-functional, the positive mass theorem and the nonuniqueness
of Ricci flow with conical initial data.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: eess