Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the
  Kahler Ricci flow   We consider the Ricci flow on $\mathbb{CP}^n$ blown-up at one point starting
with any $U(n)$-invariant K\"ahler metric. It is known that the K\"ahler-Ricci
flow must develop Type I singularities. We show that if the total volume does
not go to zero at the singular time, then any Type I parabolic blow-up limit of
the Ricci flow along the exceptional divisor is the unique $U(n)$-complete
shrinking K\"ahler-Ricci soliton on $\mathbb C^n$ blown-up at one point. This
establishes the conjecture of Feldman-Ilmanen-Knopf.

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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph