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Cauchy–Riemann meet Monge–Ampère (Q5172858)

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scientific article; zbMATH DE number 6398514

Language	Label	Description	Also known as
English	Cauchy–Riemann meet Monge–Ampère	scientific article; zbMATH DE number 6398514

Statements

scholarly article

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Cauchy–Riemann meet Monge–Ampère (English)

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Zbigniew Błocki

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Bulletin of Mathematical Sciences

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publication date

5 February 2015

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zbMATH Keywords

Bergman kernel

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Bergman distance

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Monge-Ampère equation

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Green function

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s13373-014-0058-2

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The Dirichlet problem for a complex Monge-Ampère equation

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Rolf Nevanlinna in memoriam

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The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman

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Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains

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\(L^2\)-estimates for the \(d\)-equation and Witten's proof of the Morse inequalities

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Curvature of vector bundles associated to holomorphic fibrations

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The Openness Conjecture and Complex Brunn-Minkowski Inequalities

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Densité des fonctions plurisousharmoniques

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A proof of the Ohsawa-Takegoshi theorem with sharp estimates

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Interior regularity of the complex Monge-Ampère equation in convex domains

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Equlibrium measure of a product subset of ℂⁿ

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The \(C^{1,1}\) regularity of the pluricomplex Green function

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Regularity of the pluricomplex Green function with several poles

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A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L<sup>2</sup>-estimates for the ∂-operator

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On the definition of the Monge-Ampère operator in \(\mathbb{C}^2\)

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The Bergman metric and the pluricomplex Green function

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The domain of definition of the complex Monge-Ampere operator

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Some estimates for the Bergman Kernel and Metric in Terms of Logarithmic Capacity

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Suita conjecture and the Ohsawa-Takegoshi extension theorem

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A Lower Bound for the Bergman Kernel and the Bourgain-Milman Inequality

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Estimates for $$\bar{\partial }$$ and Optimal Constants

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Hyperconvexity and Bergman completeness

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Estimates for the Bergman kernel and the multidimensional Suita conjecture

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On the Suita Conjecture for Some Convex Ellipsoids in

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The Bergman kernel function: Explicit formulas and zeroes

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New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)

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\(L^ 2\) estimates and existence theorems for the \(\partial\)-operator

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The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations

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Completeness of the Bergman metric on non-smooth pseudoconvex domains

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A remark on the bergman completeness

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Fonction de Green pluriclomplexe à pole à l'infini sur un espace de Stein parabolique et applications.

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Santaló's inequality on \(\mathbb{C}^n\) by complex interpolation

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Estimations $\mathrm{L}^2$ pour l'opérateur $\bar \partial$ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète

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Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)

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Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité. (Generalized Lelong numbers, integrability and analyticity theorems)

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Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds

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PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT KÄHLER MANIFOLDS

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Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions

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An estimate for the Bergman distance on pseudoconvex domains

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On the Bergman representative coordinates

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An example for the holomorphic sectional curvature of the Bergman metric

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\(L^ 2\)-cohomology and index theorem for the Bergman metric

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On the product property of the pluricomplex Green function

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Valuations and multiplier ideals

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The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function

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A remark on the approximation of plurisubharmonic functions

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On the Ohsawa-Takegoshi \(L^2\) extension theorem and the Bochner-Kodaira identity with non-smooth twist factor

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The structure of finite dimensional Banach spaces with the 3.2. intersection property

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The order of plurisubharmonicity on pseudoconvex domains with Lipschitz boundaries

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The Bergman metric on hyperconvex domains

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THE PLURICOMPLEX GREEN FUNCTION ON PSEUDOCONVEX DOMAINS WITH A SMOOTH BOUNDARY

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The weighted log canonical threshold

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Notions of convexity

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Invariant pseudodistances and pseudometrics - completeness and product property

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Invariant distances and metrics in complex analysis

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Bergman completeness of Zalcman type domains

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Fonctions plurisousharmoniques d'exhaustion bornees et domaines taut

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Extremal plurisubharmonic functions and invariant pseudodistances

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Geometry of Bounded Domains

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Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator

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The complex Monge-Ampère equation

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BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS

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From the Mahler conjecture to Gauss linking integrals

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La métrique de Kobayashi et la représentation des domaines sur la boule

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Variation of Bergman metrics on Riemann surfaces

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Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems

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Analytic inversion of adjunction: \(L^2\) extension theorems with gain

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Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems

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The Hörmander Proof of the Bourgain–Milman Theorem

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Conjectures of Cheng and Ramadanov

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Estimates for invariant metrics on $\mathbb C$-convex domains

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On the bergman kernel of hyperconvex domains

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Addendum to “On the Bergman kernel of hyperconvex domains”, Nagoya Math. J. 129 (1993), 43–52

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On the extension of \(L^ 2\) holomorphic functions

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On the Hessian of a function and the curvature of its graph

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Some Properties of Laplace Transforms of Measures

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Convex Bodies The Brunn-MinkowskiTheory

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Analyticity of sets associated to Lelong numbers and the extension of closed positive currents

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Extension of meromorphic maps into Kähler manifolds

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Capacities and kernels on Riemann surfaces

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On symmetrization and Hessian equations

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Domains with finite dimensional Bergman space

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Asymptotic behavior of the sectional curvature of the Bergman metric for annuli

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Regularity properties of the Azukawa metric

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An example concerning Bergman completeness

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Identifiers

zbMATH Open document ID

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10.1007/s13373-014-0058-2

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5172858

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