Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eguchi-Hanson singularities in U(2)-invariant Ricci flow   We show that a Ricci flow in four dimensions can develop singularities
modeled on the Eguchi-Hanson space. In particular, we prove that starting from
a class of asymptotically cylindrical $U(2)$-invariant initial metrics on
$TS^2$, a Type II singularity modeled on the Eguchi-Hanson space develops in
finite time. Furthermore, we show that for these Ricci flows the only possible
blow-up limits are (i) the Eguchi-Hanson space, (ii) the flat $\mathbb{R}^4
/\mathbb{Z}_2$ orbifold, (iii) the 4d Bryant soliton quotiented by
$\mathbb{Z}_2$, and (iv) the shrinking cylinder $\mathbb{R} \times \mathbb{R}
P^3$. As a byproduct of our work, we also prove the existence of a new family
of Type II singularities caused by the collapse of a two-sphere of
self-intersection $|k| \geq 3$.

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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: gr-qc