Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity

DOI10.1007/s00208-019-01936-yzbMath1460.32087arXiv1807.00276OpenAlexW2991253227MaRDI QIDQ2225604

Eleonora Di Nezza, Tamás Darvas, Chinh H. Lu

Publication date: 8 February 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.00276

zbMATH Keywords

existence and uniqueness of solutionscomplex Monge-Ampère equations

Mathematics Subject Classification ID

Complex Monge-Ampère operators (32W20)

Related Items (24)

Extremizers of the \(J\) functional with respect to the \(d_1\) metric ⋮ Geodesic distance and Monge-Ampére measures on contact sets ⋮ Complex Hessian equations with prescribed singularity on compact Kähler manifolds ⋮ Convexity of the class of currents with finite relative energy ⋮ Mabuchi geometry of big cohomology classes ⋮ Continuity method with movable singularities for classical complex Monge-Ampere equations ⋮ A complete metric topology on relative low energy spaces ⋮ Lelong numbers of currents of full mass intersection ⋮ The strong topology of \(\omega \)-plurisubharmonic functions ⋮ Volume of components of Lelong upper-level sets ⋮ Continuity of Monge-Ampère potentials with prescribed singularities ⋮ Potential theory on an analytic surface ⋮ 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 \(\mathcal{E}_{\phi}(X, \omega, m)\) ⋮ A relative Yau-Tian-Donaldson conjecture and stability thresholds ⋮ 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 ⋮ Relative non-pluripolar product of currents ⋮ Optimal asymptotic of the \(J\) functional with respect to the \(d_1\) metric ⋮ \(L^1\) 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 ⋮ Intersection theory of nefb-divisor classes ⋮ Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds

Cites Work

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• A variational approach to complex Monge-Ampère equations
• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• The space of Poincaré type Kähler metrics on the complement of a divisor
• Degenerate complex Monge-Ampère equations
• Monge-Ampère equations in big cohomology classes
• A numerical criterion for very ample line bundles
• A new capacity for plurisubharmonic functions
• Intrinsic capacities on compact Kähler manifolds
• Partial differential equations. III: Nonlinear equations.
• An inequality for mixed Monge-Ampère measures
• Uniqueness in \(\mathcal E(X,\omega)\)
• Fine topology, Šilov boundary, and \((dd^ c)^ n\)
• The Dirichlet problem for a complex Monge-Ampère equation
• The Dirichlet problem for the multidimensional Monge-Ampère equation
• Pluricomplex energy
• The complex Monge-Ampère equation
• Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity
• Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry
• Plurisubharmonic envelopes and supersolutions
• Zero distribution of random sparse polynomials
• Complex Monge-Ampère equations on quasi-projective varieties
• The weighted Monge-Ampère energy of quasiplurisubharmonic functions
• Analytic test configurations and geodesic rays
• Generalized Monge–Ampère Capacities
• Singular Kähler-Einstein metrics
• On the singularities of the pluricomplex Green's function
• Bergman kernels for weighted polynomials and weighted equilibrium measures of $\mathbb{C}^{n}$
• Differentiability of volumes of divisors and a problem of Teissier
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The Brunn-Minkowski inequality
• Pluripotential theory and convex bodies
• On the singularity type of full mass currents in big cohomology classes
• ON THE VOLUME OF A LINE BUNDLE
• Divisorial Zariski decompositions on compact complex manifolds
• Monotonicity of non-pluripolar Monge-Ampere masses
• Complete Kahler Manifolds with Zero Ricci Curvature. I

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