Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bound of modified $K$-energy on a Fano manifold with degeneration
  for K\"ahler-Ricci solitons   In this paper, we extend Tosatti's method to study the lower boundedness of
modified $K$-energy on a Fano manifold and apply this result to study the
relative $K$-stability of the deformation space of a K\"ahler Ricci soliton.

14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
7
The categories of this paper are: hep-th