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- W1444497768 abstract "Suppose $(X,J,omega)$ is a Fano manifold and $t to r_t$ is a diverging Kahler-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 Kahler-Einstein metrics. We also explore applications of our construction to Tian's $alpha$-invariant." @default.
- W1444497768 created "2016-06-24" @default.
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- W1444497768 date "2014-11-03" @default.
- W1444497768 modified "2023-09-25" @default.
- W1444497768 title "Geodesic Rays and Kahler-Ricci Trajectories on Fano Manifolds" @default.
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- W1444497768 doi "https://doi.org/10.48550/arxiv.1411.0774" @default.
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