Regularity of geodesic rays and Monge-Ampère equations

DOI10.1090/S0002-9939-10-10371-2zbMath1205.31004arXiv0908.0556WikidataQ61645884 ScholiaQ61645884MaRDI QIDQ3053509

Jacob Sturm, Duong H. Phong

Publication date: 29 October 2010

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

Full work available at URL: https://arxiv.org/abs/0908.0556

zbMATH Keywords

Kähler manifoldMonge-Ampère equationBergman geodesic

Mathematics Subject Classification ID

Pluriharmonic and plurisubharmonic functions (31C10) Local differential geometry of Hermitian and Kählerian structures (53B35)

Related Items (19)

From Monge-Ampère equations to envelopes and geodesic rays in the zero temperature limit ⋮ Geodesic rays and stability in the lowercase cscK problem ⋮ Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity ⋮ On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics ⋮ Envelopes of positive metrics with prescribed singularities ⋮ \(L^1\) metric geometry of big cohomology classes ⋮ Geometric flow, multiplier ideal sheaves and optimal destabilizer for a Fano manifold ⋮ Mabuchi's soliton metric and relative D-stability ⋮ Calabi type functionals for coupled Kähler-Einstein metrics ⋮ The Kähler-Ricci flow and optimal degenerations ⋮ Geodesic rays and Kähler–Ricci trajectories on Fano manifolds ⋮ The Dirichlet problem for the complex homogeneous Monge-Ampère equation ⋮ Kähler-Einstein metrics ⋮ C^1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays ⋮ Test configurations and Okounkov bodies ⋮ C1,1 regularity of geodesics of singular Kähler metrics ⋮ Moment maps, nonlinear PDE and stability in mirror symmetry. I: Geodesics ⋮ The closures of test configurations and algebraic singularity types ⋮ K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics

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