Mabuchi geometry of big cohomology classes

DOI10.1515/crelle-2023-0019zbMath1522.53062OpenAlexW4367055073MaRDI QIDQ6042650

Mingchen Xia

Publication date: 3 May 2023

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle-2023-0019

zbMATH Keywords

plurisubharmonic functionsKähler manifoldsMonge-Ampére equations

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Moduli problems for differential geometric structures (58D27) Kähler manifolds (32Q15) CR structures, CR operators, and generalizations (32V05) Complex Monge-Ampère operators (32W20) Monge-Ampère equations (35J96)

Related Items (1)

A relative Yau-Tian-Donaldson conjecture and stability thresholds

Cites Work

• Degenerate complex Monge-Ampère equations
• Monge-Ampère equations in big cohomology classes
• The Mabuchi geometry of finite energy classes
• The space of Kähler metrics.
• 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
• \(L^p\) metric geometry of big and nef cohomology classes
• \(L^1\) metric geometry of potentials with prescribed singularities on compact Kähler manifolds
• The closures of test configurations and algebraic singularity types
• The metric geometry of singularity types
• Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry
• Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
• The weighted Monge-Ampère energy of quasiplurisubharmonic functions
• On regularization of plurisubharmonic functions on manifolds
• On the singularity type of full mass currents in big cohomology classes
• C^1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays
• Comparison of Monge–Ampère capacities
• Convexity of the class of currents with finite relative energy
• A variational approach to the Yau–Tian–Donaldson conjecture
• Geometric pluripotential theory on Kähler manifolds
• Monotonicity of non-pluripolar Monge-Ampere masses
• Möbius orthogonality for generalized Morse-Kakutani flows

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