Mabuchi's soliton metric and relative D-stability

DOI10.1353/ajm.2023.a897496zbMath1528.53065arXiv1905.05948WikidataQ125325067 ScholiaQ125325067MaRDI QIDQ6135853

Tomoyuki Hisamoto

Publication date: 28 August 2023

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05948

zbMATH Keywords

Kähler-Einstein metricFano manifoldMonge-Ampere equationMabuchi metricMabuchi soliton

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Fano varieties (14J45) Kähler-Einstein manifolds (32Q20)

Related Items (5)

On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations ⋮ Calabi type functionals for coupled Kähler-Einstein metrics ⋮ Anticanonically balanced metrics and the Hilbert-Mumford criterion for the \(\delta_m\)-invariant of Fujita-Odaka ⋮ A relative Yau-Tian-Donaldson conjecture and stability thresholds ⋮ Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold
• Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
• Kähler-Einstein metrics along the smooth continuity method
• A variational approach to complex Monge-Ampère equations
• Degenerate complex Monge-Ampère equations
• On the extension of \(L^ 2\) holomorphic functions
• Monge-Ampère equations in big cohomology classes
• A new holomorphic invariant and uniqueness of Kähler-Ricci solitons
• The Mabuchi geometry of finite energy classes
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• Growth of balls of holomorphic sections and energy at equilibrium
• Optimal test-configurations for toric varieties
• On some integral invariants on complex manifolds. I
• K-energy maps integrating Futaki invariants
• Some symplectic geometry on compact Kähler manifolds. I
• Remarks on the existence problem of positive Kähler-Einstein metrics
• Kähler-Einstein metrics and the generalized Futaki invariant
• The Dirichlet problem for a complex Monge-Ampère equation
• Pluricomplex energy
• Moment maps and combinatorial invariants of Hamiltonian \(T^ n\)-spaces
• Bilinear forms and extremal Kähler vector fields associated with Kähler classes
• Kähler-Einstein metrics with positive scalar curvature
• The space of Kähler metrics.
• On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics
• Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs
• Scalar curvature and stability of toric varieties.
• An obstruction to the existence of Einstein Kaehler metrics
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Regularity of weak solutions of a complex Monge-Ampère equation
• The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics
• \(G\)-uniform stability and Kähler-Einstein metrics on Fano varieties
• Relative Ding stability and an obstruction to the existence of Mabuchi solitons
• Generalized Kähler Einstein metrics and uniform stability for toric Fano manifolds
• The Kähler-Ricci flow and optimal degenerations
• Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry
• On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows
• Special test configuration and \(K\)-stability of Fano varieties
• Uniqueness of \(\mathrm{K}\)-polystable degenerations of Fano varieties
• Mabuchi metrics and properness of the modified Ding functional
• Uniform K-stability and asymptotics of energy functionals in Kähler geometry
• The moduli space of Fano manifolds with Kähler-Ricci solitons
• A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
• Curvature of vector bundles associated to holomorphic fibrations
• Convexity of the extended K-energy and the large time behavior of the weak Calabi flow
• Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
• A valuative criterion for uniform K-stability of \(\mathbb{Q}\)-Fano varieties
• A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
• The weighted Monge-Ampère energy of quasiplurisubharmonic functions
• Test configurations for \(k\)-stability and geodesic rays
• Lower bounds on the Calabi functional
• Analytic test configurations and geodesic rays
• Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics
• Viscosity solutions to degenerate complex monge-ampère equations
• Regularity of geodesic rays and Monge-Ampère equations
• Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
• A study of the Hilbert-Mumford criterion for the stability of projective varieties
• Complex Monge-Ampere and Symplectic Manifolds
• Multiplier Hermitian structures on Kähler manifolds
• Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
• C^1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays
• Hessian of the Ricci-Calabi functional
• Test configurations and Okounkov bodies
• VARIATIONAL AND NON-ARCHIMEDEAN ASPECTS OF THE YAU–TIAN–DONALDSON CONJECTURE
• A variational approach to the Yau–Tian–Donaldson conjecture
• K‐Stability and Kähler‐Einstein Metrics
• The Ding Functional, Berndtsson Convexity and Moment Maps
• Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
• Test configurations and Geodesic rays
• WEAK GEODESIC RAYS IN THE SPACE OF KÄHLER POTENTIALS AND THE CLASS
• Möbius orthogonality for generalized Morse-Kakutani flows
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• Mabuchi Solitons and Relative Ding Stability of Toric Fano Varieties
• Kähler-Einstein metrics for manifolds with nonvanishing Futaki character
• On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations

This page was built for publication: Mabuchi's soliton metric and relative D-stability