A global estimate for the Diederich-Fornaess index of weakly pseudoconvex domains

DOI10.1215/00277630-3335655zbMath1334.32013arXiv1401.2264OpenAlexW1652989718MaRDI QIDQ2788614

Masanori Adachi, Judith Brinkschulte

Publication date: 19 February 2016

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.2264

zbMATH Keywords

Diederich-Fornaess index\(\overline{\partial}\)-equation with regularity on pseudoconvex domains

Mathematics Subject Classification ID

Real submanifolds in complex manifolds (32V40) CR manifolds as boundaries of domains (32V15)

Related Items

Bergman kernel and hyperconvexity index ⋮ A CR Proof for a Global Estimate of the Diederich–Fornaess Index of Levi-Flat Real Hypersurfaces ⋮ The Diederich-Fornaess index and the regularities on the \bar{\partial}-Neumann problem ⋮ The intrinsic geometry on bounded pseudoconvex domains ⋮ Weakly 1‐completeness of holomorphic fiber bundles over compact Kähler manifolds ⋮ The core of the Levi distribution ⋮ Estimates for \(\overline{\partial}\) on domains in \(\mathbb{C}^n\) and \(\mathbb{CP}^n\) ⋮ The Diederich-Fornæss index. II: For domains of trivial index ⋮ On the dimension of the Bergman space for some unbounded domains ⋮ Geometric Analysis on the Diederich-Forn{\ae}ss Index ⋮ Bounded plurisubharmonic exhaustion functions and Levi-flat hypersurfaces ⋮ Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes ⋮ On weighted Bergman spaces of a domain with Levi-flat boundary ⋮ The Diederich-Fornæss index. I: For domains of non-trivial index ⋮ A local expression of the Diederich-Fornaess exponent and the exponent of conformal harmonic measures

Cites Work

• A log-Sobolev type inequality for free entropy of two projections
• Pseudoconvex domains: An example with nontrivial nebenhuelle
• Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions
• A Sobolev mapping property of the Bergman kernel
• The \(\bar \partial\)-problem with support conditions on some weakly pseudoconvex domains
• Estimates for the \(\bar\partial\)-Neumann problem and nonexistence of \(C^2\) Levi-flat hypersurfaces in \(\mathbb{C} P^n\)
• On the ampleness of positive CR line bundles over Levi-flat manifolds
• The strong Oka's lemma, bounded plurisubharmonic functions and the \(\overline\partial\)-Neumann problem
• $L^{2}$ Serre duality on domains in complex manifolds and applications
• Bounded p.s.h. functions and pseudoconvexity in Kähler manifold

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