The Donnelly-Fefferman theorem on \(q\)-pseudoconvex domains

zbMath1214.32015MaRDI QIDQ1043679

Nguyen Quang Dieu, HeungJu Ahn

Publication date: 9 December 2009

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1256564197

zbMATH Keywords

plurisubharmonic functionsintegral estimatesapproximation of forms

Mathematics Subject Classification ID

(q)-convexity, (q)-concavity (32F10) (overlinepartial) and (overlinepartial)-Neumann operators (32W05)

Related Items (10)

The \(\bar{\partial}\)-Neumann problem on the intersection of two weakly \(q\)-convex domains ⋮ Existence and compactness for the \(\overline\partial\)-Neumann operator on \(q\)-convex domains ⋮ Maximal \(q\)-subharmonicity in \(\mathbb{C}^n\) ⋮ On compactness of the \(\bar{\partial}\)-Neumann operator on \(r\)-convex domains ⋮ \(L^{2}\)-approximation of differential forms by \(\bar {\partial}\)-closed ones on smooth hypersurfaces ⋮ Unnamed Item ⋮ \(L^2\) estimates and existence theorems for \(\overline{\partial}_b\) on Lipschitz boundaries of \(Q\)-pseudoconvex domains ⋮ The $$\overline \partial $$ -Neumann operator on Lipschitz q-pseudoconvex domains ⋮ \(L^{2}\)-estimates on weakly \(q\)-convex domains ⋮ Continuous \(\omega^q\)-plurisubharmonic exhaustion functions on Kähler manifolds

Cites Work

• \({\bar \partial}\)-problem on weakly \(q\)-convex domains
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• \(q\)-plurisubharmonicity and \(q\)-pseudoconvexity in \(\mathbb C^n\)
• The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman
• The Bergman metric and the pluricomplex Green function

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