The weighted Monge-Ampère energy of quasiplurisubharmonic functions

From MaRDI portal
Publication:2456992

DOI10.1016/j.jfa.2007.04.018zbMath1143.32022arXivmath/0612630OpenAlexW2067250917WikidataQ126247664 ScholiaQ126247664MaRDI QIDQ2456992

Vincent Guedj, Ahmed Zeriahi

Publication date: 29 October 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612630



Related Items

Pluripotential theory on compact Hermitian manifolds, The Dini type condition in the existence of continuous solutions to the complex Monge-Ampère equations on compact Kähler manifolds, Continuous solutions to Monge-Ampère equations on Hermitian manifolds for measures dominated by capacity, Weighted regularity and two problems of Sadullaev on weighted regularity, Convergence of the Kähler-Ricci iteration, A note on the space of delta \(m\)-subharmonic functions, Extremal potentials and equilibrium measures for collections of Kähler classes, Continuity of the complex Monge-Ampère operator on compact Kähler manifolds, Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity, Extremizers of the \(J\) functional with respect to the \(d_1\) metric, Geodesic distance and Monge-Ampére measures on contact sets, On the boundary behavior of Kähler-Einstein metrics on log canonical pairs, General weak limit for Kähler–Ricci flow, Subharmonicity of conic Mabuchi’s functional, I, Uniqueness and short time regularity of the weak Kähler-Ricci flow, Weighted pluricomplex energy, A variational approach to complex Monge-Ampère equations, Complex Monge-Ampère equations on quasi-projective varieties, Regularizing properties of the twisted Kähler-Ricci flow, An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms, Approximation of weak geodesics and subharmonicity of Mabuchi energy, Convexity of the extended K-energy and the large time behavior of the weak Calabi flow, Geometric pluripotential theory on Sasaki manifolds, A product property for the pluricomplex energy, Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds, Solutions to degenerate complex Hessian equations, Local geodesics for plurisubharmonic functions, Envelopes of positive metrics with prescribed singularities, The Mabuchi geometry of finite energy classes, A viscosity approach to degenerate complex Monge-Ampère equations, Comparison of the Calabi and Mabuchi geometries and applications to geometric flows, Regularity of push-forward of Monge-Ampère measures, \(L^1\) metric geometry of big cohomology classes, The complex Monge-Ampère type equation on compact Hermitian manifolds and applications, Monge-Ampère equations in big cohomology classes, Some weighted energy classes of plurisubharmonic functions, Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties, Weak solutions to complex Monge-Ampère equations on compact Kähler manifolds, Supports of weighted equilibrium measures and examples, Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics, Symmetrization of plurisubharmonic functions and Fano manifolds, A complete metric topology on relative low energy spaces, Curvature of the completion of the space of Sasaki potentials, On the singularity type of full mass currents in big cohomology classes, Geometric methods of complex analysis. Abstracts from the workshop held May 16--22, 2021 (hybrid meeting), Differential geometry in the large (hybrid meeting). Abstracts from the workshop held July 4--10, 2021 (hybrid meeting), Logarithmic potentials on \(\mathbb{P}^n\), Maximal subextensions of plurisubharmonic functions, A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics, Geodesic rays and Kähler–Ricci trajectories on Fano manifolds, Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry, Determinantal point processes and fermions on complex manifolds: large deviations and bosonization, Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampère operator, The long-time behavior of modified Calabi flow, Pluripotential energy, Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity, Kähler-Einstein metrics on stable varieties and log canonical pairs, Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor, Tian’s Properness Conjectures:An Introduction to Kähler Geometry, On some classes of \(\omega\)-plurisubharmonic functions on compact Kähler manifolds, Cusp Kähler-Ricci flow on compact Kähler manifolds, \(C^{1,1}\) regularity of degenerate complex Monge-Ampère equations and some applications, On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows, Regularizing properties of complex Monge-Ampère flows, Choquet-Monge-Ampère classes, \(L^p\) metric geometry of big and nef cohomology classes, Viscosity solutions to degenerate complex monge-ampère equations, Extremal \(\omega \)-plurisubharmonic functions as~envelopes of disc functionals, The complex Monge-Ampère equation on compact Kähler manifolds, Domains of definition of Monge-Ampère operators on compact Kähler manifolds, Mass equidistribution for random polynomials, Some new estimates for the complex Monge-Ampère equation, Special metrics in Kähler geometry, Geometry and topology of the space of Kähler metrics on singular varieties, Finite entropy vs finite energy, Relative non-pluripolar product of currents, Singular Kähler-Einstein metrics, An inequality for mixed Monge-Ampère measures, Uniqueness in \(\mathcal E(X,\omega)\), On a Monge-Ampere operator for plurisubharmonic functions with analytic singularities, Compactness of Kähler metrics with bounds on Ricci curvature and \({\mathcal{I}}\) functional, Global and local definition of the Monge-Ampère operator on compact Kähler manifolds, The Non-Archimedean Monge–Ampère Equation, Modulability and duality of certain cones in pluripotential theory, Optimal asymptotic of the \(J\) functional with respect to the \(d_1\) metric, \(\mathrm{klt}\) varieties with trivial canonical class: holonomy, differential forms, and fundamental groups, The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics, On the Moser-Trudinger inequality in complex space, \(G\)-uniform stability and Kähler-Einstein metrics on Fano varieties, The closures of test configurations and algebraic singularity types, Quasiplurisubharmonic Green functions, The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties, KÄHLER–EINSTEIN METRICS WITH CONE SINGULARITIES ON KLT PAIRS, Non-pluripolar energy and the complex Monge-Ampère operator, Mixed Hessian inequalities and uniqueness in the class \(\mathcal {E}(X,\omega ,m)\), EQUIDISTRIBUTION TOWARD THE GREEN CURRENT IN BIG COHOMOLOGY CLASSES, On the weighted \(m\)-energy classes, Orbifold stability and Miyaoka-Yau inequality for minimal pairs, A variational approach to complex Hessian equations in \(\mathbb{C}^n\), Stability of Monge-Ampère energy classes, Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics, Complex Hessian equations with prescribed singularity on compact Kähler manifolds, Generalized Kähler-Ricci flow on toric Fano varieties, Convexity of the class of currents with finite relative energy, Extremal metrics on toric manifolds and homogeneous toric bundles, Mabuchi geometry of big cohomology classes, On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations, Weighted K-stability and coercivity with applications to extremal Kähler and Sasaki metrics, Quasi-monotone convergence of plurisubharmonic functions, A characterization of the degenerate complex Hessian equations for functions with bounded (p,m)-energy, On the regularity of conical Calabi–Yau potentials, On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows, Projective logarithmic potentials, Mabuchi's soliton metric and relative D-stability, Lelong numbers of currents of full mass intersection, The strong topology of \(\omega \)-plurisubharmonic functions, Families of singular Kähler-Einstein metrics, Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's ``hypothèse fondamentale, Global pluripotential theory over a trivially valued field, Uniform estimates for cscK metrics, Continuous solutions for degenerate complex Hessian equation, Complex analysis -- differential and algebraic methods in Kähler spaces. Abstracts from the workshop held April 9--14, 2023, Weak solutions to complex Hessian type equations in the class \(\mathcal{E}_{\phi}(X, \omega, m)\), Weakly Kähler hyperbolic manifolds and the Green-Griffiths-Lang conjecture, Emergent complex geometry, A relative Yau-Tian-Donaldson conjecture and stability thresholds, WEAK GEODESIC RAYS IN THE SPACE OF KÄHLER POTENTIALS AND THE CLASS, On the constant scalar curvature Kähler metrics (II)—Existence results, WEAK CONTINUITY OF THE COMPLEX -HESSIAN OPERATORS WITH RESPECT TO LOCAL UNIFORM CONVERGENCE, A variational approach to the Yau–Tian–Donaldson conjecture, Open problems in pluripotential theory, Finite pluricomplex energy measures, On a characterization of $m$-subharmonic functions with weak singularities, Toric pluripotential theory, Geometric pluripotential theory on Kähler manifolds, Equidistribution of non-pluripolar products associated with quasi-plurisubharmonic functions of finite energy, Monotonicity of non-pluripolar Monge-Ampere masses, Duality between the pseudoeffective and the movable cone on a projective manifold, On Calabi’s extremal metric and properness, Comparison of Monge–Ampère capacities, Density currents and relative non‐pluripolar products, Solution to a non-Archimedean Monge-Ampère equation



Cites Work