Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ancient solutions to the Ricci flow in higher dimensions   In this paper, we study $\kappa$-noncollapsed ancient solutions to the Ricci
flow with nonnegative curvature operator in higher dimensions. We impose one
further assumption: one of the asymptotic shrinking gradient Ricci solitons is
the standard cylinder $\mathbb{S}^{n-1}\times\mathbb{R}$. By making use of the
properties of such ancient solutions, we generalize part one of Brendle
\cite{brendle2018ancient} to higher dimensions, that is, every noncompact
$\kappa$-noncollapsed rotationally symmetric ancient solution to the Ricci flow
with bounded positive curvature operator must be the Bryant soliton.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex