Integral representations on Hermitian manifolds: the ∂̄-Neumann solution of the Cauchy-Riemann equations

DOI10.1090/S0273-0979-1984-15305-9zbMath0574.35066OpenAlexW1530097612MaRDI QIDQ3693950

Ingo Lieb, R. Michael Range

Publication date: 1984

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1984-15305-9

zbMATH Keywords

Hermitian manifoldexplicit formulasharp estimatesLevi metric\({\bar \partial }\)-Neumann problemNeumann operatorCauchy Riemann complex

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Integral representations of solutions to PDEs (35C15) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

Fixed point formula for holomorphic functions

Cites Work

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• The \(\bar\partial\)-Neumann operator on the unit ball in \({\mathbb C}^n\)
• The solution of the (partial d)-Neumann problem in a strictly pseudoconvex Siegel domain
• The Szegö kernel in terms of Cauchy-Fantappie kernels
• Subellipticity of the \(\overline\partial\)-Neumann problem on pseudo- convex domains: sufficient conditions
• On integral representations and a priori Lipschitz estimates for the canonical solution of the \(\partial\)-equation
• Harmonic integrals on strongly pseudo-convex manifolds. I
• The $\overline \partial$-Neumann Solution to the Inhomogeneous Cauchy-Riemann Equation in the Ball in $C^n$
• The Hölder continuity of the Bergman projection and proper holomorphic mappings
• On integral representations for the Neumann operator

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