On the singularity type of full mass currents in big cohomology classes

DOI10.1112/S0010437X1700759XzbMath1398.32042arXiv1606.01527OpenAlexW2412985804MaRDI QIDQ4602850

Eleonora Di Nezza, Tamás Darvas, Chinh H. Lu

Publication date: 7 February 2018

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.01527

zbMATH Keywords

complex Monge-Ampère equationbig cohomology classfinite energy class

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05)

Related Items (27)

The metric geometry of singularity types ⋮ Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity ⋮ Geodesic distance and Monge-Ampére measures on contact sets ⋮ Complex Hessian equations with prescribed singularity on compact Kähler manifolds ⋮ Rooftop envelopes and residual plurisubharmonic functions ⋮ Envelopes with prescribed singularities ⋮ Convexity of the class of currents with finite relative energy ⋮ Stability of solutions to complex Monge-Ampère flows ⋮ \(L^1\) metric geometry of big cohomology classes ⋮ Mabuchi geometry of big cohomology classes ⋮ Quasi-monotone convergence of plurisubharmonic functions ⋮ A complete metric topology on relative low energy spaces ⋮ Lelong numbers of currents of full mass intersection ⋮ Families of singular Kähler-Einstein metrics ⋮ Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's ``hypothèse fondamentale ⋮ A relative Yau-Tian-Donaldson conjecture and stability thresholds ⋮ Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry ⋮ Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity ⋮ \(L^p\) metric geometry of big and nef cohomology classes ⋮ Geometry and topology of the space of Kähler metrics on singular varieties ⋮ C1,1 regularity of geodesics of singular Kähler metrics ⋮ Relative non-pluripolar product of currents ⋮ Monotonicity of non-pluripolar Monge-Ampere masses ⋮ \(L^1\) metric geometry of potentials with prescribed singularities on compact Kähler manifolds ⋮ Comparison of Monge–Ampère capacities ⋮ Kähler-Einstein metrics with prescribed singularities on Fano manifolds ⋮ Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds

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