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

DOI10.1007/978-3-319-09477-9_4zbMath1321.32003OpenAlexW853391929MaRDI QIDQ5255110

Zbigniew Błocki

Publication date: 11 June 2015

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-09477-9_4

zbMATH Keywords

Bergman kernellogarithmic capacitypluricomplex Green functionSuita conjectureBourgain-Milman inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items

Complex Brunn-Minkowski inequalities and their applications in geometry, Estimates of the Bergman kernel on Teichmüller space, On Nazarov’s Complex Analytic Approach to the Mahler Conjecture and the Bourgain-Milman Inequality, A Survey on Bergman Completeness, Complex geodesics in tube domains and their role in the study of harmonic mappings in the disc, Bergman–Toeplitz operators on fat Hartogs triangles, Suita Conjecture from the One-dimensional Viewpoint, Convex floating bodies as approximations of Bergman sublevel sets on tube domains, Transport proofs of some functional inverse Santaló inequalities, Optimal \(L^2\) extensions of openness type and related topics, One dimensional estimates for the Bergman kernel and logarithmic capacity, Real and complex Brunn-Minkowski theory, A Counterexample to a Conjecture by Błocki–Zwonek, Further remarks on the higher dimensional Suita conjecture, On the Błocki-Zwonek conjectures and beyond, Generalizations of the higher dimensional Suita conjecture and its relation with a problem of Wiegerinck, Cauchy–Riemann meet Monge–Ampère, Estimates for $$\bar{\partial }$$ and Optimal Constants, A proof of Saitoh's conjecture for conjugate Hardy \(H^2\) kernels, Remarks on the higher dimensional Suita conjecture, A remark on Carleson measures of domains in ℂⁿ, Carleson measures on the generalized Hartogs triangles

Cites Work

• Unnamed Item
• Unnamed Item
• Complex geodesics in convex tube domains. II
• Suita conjecture and the Ohsawa-Takegoshi extension theorem
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• From the Mahler conjecture to Gauss linking integrals
• Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)
• Holomorphic invariants, normal forms, and the moduli space of convex domains
• The Bergman metric on hyperconvex domains
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Capacities and kernels on Riemann surfaces
• Estimates for $$\bar{\partial }$$ and Optimal Constants
• La métrique de Kobayashi et la représentation des domaines sur la boule
• Invariant pseudodistances and pseudometrics - completeness and product property
• On the product property of the pluricomplex Green function
• The Bergman metric and the pluricomplex Green function
• A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for the ∂-operator
• The Hörmander Proof of the Bourgain–Milman Theorem
• Some Properties of Laplace Transforms of Measures