Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The K\"ahler-Ricci flow and quantitative bounds for Donaldson-Futaki
  invariants of optimal degenerations   We establish a lower bound for the Donaldson-Futaki invariant of optimal
degenerations produced by the K\"ahler-Ricci flow in terms of the greatest
Ricci lower bound on arbitrary Fano manifolds. As an application, we can
generalize the finiteness of the Futaki invariants on K\"ahler-Ricci solitons
obtained by Guo-Phong-Song-Sturm to the space of all Fano manifolds. Also, we
discuss the relation to Hisamoto's inequality for the infimum of the
$H$-functional.

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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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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: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin