Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci flow neckpinches without rotational symmetry   We study "warped Berger" solutions $\big(\mc S^1\times\mc S^3,G(t)\big)$ of
Ricci flow: generalized warped products with the metric induced on each fiber
$\{s\}\times\mathrm{SU}(2)$ a left-invariant Berger metric. We prove that this
structure is preserved by the flow, that these solutions develop finite-time
neckpinch singularities, and that they asymptotically approach round product
metrics in space-time neighborhoods of their singular sets, in precise senses.
These are the first examples of Ricci flow solutions without rotational
symmetry that become asymptotically rotationally symmetric locally as they
develop local finite-time singularities.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: supr-con