Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry

DOI10.2140/gt.2020.24.1907zbMath1479.32011arXiv1810.04661OpenAlexW3102878547WikidataQ125116283 ScholiaQ125116283MaRDI QIDQ2211891

Tamás Darvas, Chinh H. Lu

Publication date: 17 November 2020

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04661

zbMATH Keywords

stabilityKähler metricsMabuchi rays

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Plurisubharmonic functions and generalizations (32U05) Notions of stability for complex manifolds (32Q26)

Related Items (20)

The isometries of the space of Kähler metrics ⋮ Geodesic rays and stability in the lowercase cscK problem ⋮ Extremizers of the \(J\) functional with respect to the \(d_1\) metric ⋮ Geodesic distance and Monge-Ampére measures on contact sets ⋮ Extremal metrics on toric manifolds and homogeneous toric bundles ⋮ Mabuchi 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 ⋮ Extremal Kähler metrics of toric manifolds ⋮ A relative Yau-Tian-Donaldson conjecture and stability thresholds ⋮ The space of finite-energy metrics over a degeneration of complex manifolds ⋮ Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity ⋮ Geometric quantization of coupled Kähler-Einstein metrics ⋮ On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows ⋮ Geometric pluripotential theory on Kähler manifolds ⋮ Valuative invariants with higher moments ⋮ Optimal asymptotic of the \(J\) functional with respect to the \(d_1\) metric ⋮ The closures of test configurations and algebraic singularity types ⋮ Comparison of Monge–Ampère capacities ⋮ Plurisubharmonic geodesics in spaces of non-Archimedean metrics of finite energy

Cites Work

• Unnamed Item
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• Uniqueness and short time regularity of the weak Kähler-Ricci flow
• A variational approach to complex Monge-Ampère equations
• Uniformly convex metric spaces
• Monge-Ampère equations in big cohomology classes
• Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
• Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité
• Intrinsic capacities on compact Kähler manifolds
• The Mabuchi geometry of finite energy classes
• On a set of polarized Kähler metrics on algebraic manifolds
• Hamiltonian 2-forms in Kähler geometry. III: Extremal metrics and stability
• On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
• Some symplectic geometry on compact Kähler manifolds. I
• The partial Legendre transformation for plurisubharmonic functions
• Sharp uniform convexity and smoothness inequalities for trace norms
• Kähler-Einstein metrics with positive scalar curvature
• Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
• The complex Monge-Ampère equation
• 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
• Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs
• The space of Kähler metrics. II.
• Scalar curvature and stability of toric varieties.
• An obstruction to the existence of Einstein Kaehler metrics
• The K-energy on hypersurfaces and stability
• The metric geometry of singularity types
• The Kähler-Ricci flow and optimal degenerations
• Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
• Special test configuration and \(K\)-stability of Fano varieties
• Compactness of Kähler metrics with bounds on Ricci curvature and \({\mathcal{I}}\) functional
• Uniform K-stability and asymptotics of energy functionals in Kähler geometry
• Weak geodesics in the space of Kähler metrics
• Regularizing properties of the twisted Kähler-Ricci flow
• Convexity of the extended K-energy and the large time behavior of the weak Calabi flow
• Probability measures associated to geodesics in the space of Kähler metrics
• Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
• Jensen's inequality on convex spaces
• The weighted Monge-Ampère energy of quasiplurisubharmonic functions
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Analytic test configurations and geodesic rays
• Convexities of metric spaces
• Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions
• The Complex Monge–Ampère Equation in Kähler Geometry
• Regularizing Properties of the Kähler–Ricci Flow
• Space of Kähler Metrics (V) – Kähler Quantization
• Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics
• Geodesic rays and Kähler–Ricci trajectories on Fano manifolds
• Poincaré inequalities, embeddings, and wild groups
• On regularization of plurisubharmonic functions on manifolds
• Scalar curvature and projective embeddings, II
• Complex Monge-Ampere and Symplectic Manifolds
• Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
• On the singularity type of full mass currents in big cohomology classes
• Geometry and topology of the space of Kähler metrics on singular varieties
• Regularity of weak minimizers of the K-energy and applications to properness and K-stability
• Quantization in Geometric Pluripotential Theory
• VARIATIONAL AND NON-ARCHIMEDEAN ASPECTS OF THE YAU–TIAN–DONALDSON CONJECTURE
• Geometric pluripotential theory on Kähler manifolds
• Monotonicity of non-pluripolar Monge-Ampere masses
• On Calabi’s extremal metric and properness
• Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
• WEAK GEODESIC RAYS IN THE SPACE OF KÄHLER POTENTIALS AND THE CLASS
• On the Space of Kähler Potentials
• Uniformly Convex Spaces

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