Geodesic rays and Kähler–Ricci trajectories on Fano manifolds

DOI10.1090/tran/6878zbMath1366.53052arXiv1411.0774OpenAlexW2964118789MaRDI QIDQ2975782

Tamás Darvas, Weiyong He

Publication date: 12 April 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.0774

zbMATH Keywords

Kähler manifoldFano manifoldfunctionalsspecial Kähler metricsspace of Kähler potentialsAubin-Mabuchi energyDing's functionalTian's alpha-invariant

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Fano varieties (14J45) Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05) Manifolds of metrics (especially Riemannian) (58D17)

Related Items

Geodesic rays and stability in the lowercase cscK problem, Convexity of the extended K-energy and the large time behavior of the weak Calabi flow, The Mabuchi geometry of finite energy classes, Comparison of the Calabi and Mabuchi geometries and applications to geometric flows, \(L^1\) metric geometry of big cohomology classes, Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics, Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties, Geometric flow, multiplier ideal sheaves and optimal destabilizer for a Fano manifold, Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry, Tian’s Properness Conjectures:An Introduction to Kähler Geometry, C^1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays, On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows, On the constant scalar curvature Kähler metrics (II)—Existence results, A variational approach to the Yau–Tian–Donaldson conjecture, Kähler-Ricci flow, Kähler-Einstein metric, and K-stability, Geometric pluripotential theory on Kähler manifolds, \(L^1\) metric geometry of potentials with prescribed singularities on compact Kähler manifolds, The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties, K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics

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