Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic Rays and K\"ahler-Ricci Trajectories on Fano Manifolds   Suppose $(X,J,\omega)$ is a Fano manifold and $t \to r_t$ is a diverging
K\"ahler-Ricci trajectory. We construct a bounded geodesic ray $t \to u_t$
weakly asymptotic to $t \to r_t$, along which Ding's $\mathcal F$-functional
decreases, partially confirming a folklore conjecture. In absence of
non-trivial holomorphic vector fields this proves the equivalence between
geodesic stability of the $\mathcal F$-functional and existence of
K\"ahler-Einstein metrics. We also explore applications of our construction to
Tian's $\alpha$-invariant.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph