De Rham cohomology of manifolds containing the points of infinite type, and Sobolev estimates for the \(\bar \partial\)-Neumann problem

DOI10.1007/BF02921391zbMath0792.32013OpenAlexW2323641579WikidataQ57376097 ScholiaQ57376097MaRDI QIDQ685947

Harold P. Boas, Emil J. Straube

Publication date: 28 July 1994

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921391

zbMATH Keywords

Sobolev spacede Rham cohomology\(\overline \partial\)-Neumann problem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) de Rham theory in global analysis (58A12) (overlinepartial) and (overlinepartial)-Neumann operators (32W05)

Related Items

The Diederich-Fornaess index and the regularities on the \bar{\partial}-Neumann problem ⋮ The intrinsic geometry on bounded pseudoconvex domains ⋮ CR-invariance of the Steinness index ⋮ The core of the Levi distribution ⋮ L2-Sobolev theory for the complex Green operator ⋮ The Diederich-Fornæss index. II: For domains of trivial index ⋮ The Kohn-Laplace equation on abstract CR manifolds: Global regularity ⋮ Semi-continuity of the Diederich–Fornaess and Steinness indices ⋮ Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type ⋮ A sufficient condition for global regularity of the \(\bar {\partial}\)-Neumann operator ⋮ Regularity of canonical operators and Nebenhülle: Hartogs domains ⋮ Hartogs domains and the Diederich-Fornæss index ⋮ Analytic discs, plurisubharmonic hulls, and non-compactness of the \(\bar\partial\)-Neumann operator ⋮ Geometric Analysis on the Diederich-Forn{\ae}ss Index ⋮ Regularity of the Bergman projection on forms and plurisubharmonicity conditions ⋮ Proper Holomorphic Mappings and the Cowen-Douglas Class ⋮ The ∂¯-Neumann operator with Sobolev estimates up to a finite order ⋮ Diederich-Fornæss and Steinness indices for abstract CR manifolds ⋮ The Diederich-Fornæss index. I: For domains of non-trivial index ⋮ The Diederich-Fornaess index and good vector fields ⋮ On competing definitions for the Diederich-Fornæss index ⋮ Local plurisubharmonic defining functions on the boundary ⋮ Strong Stein neighbourhood bases ⋮ Levi foliations in pseudoconvex boundaries and vector fields that commute approximately with $\bar \partial $

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