Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted and conical K\"ahler-Ricci soliton on Fano manifolds   In this paper, we consider the twisted K\"ahler-Ricci soliton, and show that
the existence of twisted K\"ahler-Ricci soliton with semi-positive twisting
form is closely related to the properness of some energy functionals. We also
consider the conical K\"ahler-Ricci soliton, and obtain some existence results.
In particular, under some assumptions on the divisor and $\alpha$-invariant, we
get the properness of the modified log K-energy and the existence of conical
K\"ahler-Ricci soliton with suitable cone angle.

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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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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: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: nlin