On the infinite dimensionality of the middle \(L^ 2\) cohomology of complex domains

DOI10.2977/prims/1195173354zbMath0706.32004OpenAlexW1980257473MaRDI QIDQ919145

Takeo Ohsawa

Publication date: 1989

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195173354

zbMATH Keywords

Stein manifoldhermitian metricbounded domainstrictly pseudoconvex domaincomplex manifold\(L^ 2\)- cohomologyinfinite dimensionality

Mathematics Subject Classification ID

Differential forms in global analysis (58A10) Stein spaces (32E10) Analytic spaces (32C99) Pseudoconvex domains (32T99) Local cohomology of analytic spaces (32C36)

Related Items (6)

Remarks on the metric induced by the Robin function III ⋮ Infinite dimensionality of the middle \(L^2\)-cohomology on non-compact Kähler hyperbolic manifolds ⋮ Bott-Chern harmonic forms on Stein manifolds ⋮ Bott–Chern harmonic forms on complete Hermitian manifolds ⋮ Comments on the Green's function of a planar domain ⋮ \(L^2\)-cohomology vanishing theorem on a type of generalized Cartan-Hartogs domain

Cites Work

• On the extension of \(L^ 2\) holomorphic functions
• Hodge spectral sequence on compact Kähler spaces
• Hodge spectral sequence and symmetry on compact Kähler spaces
• Hodge spectral sequence on pseudoconvex domains
• The Hodge cohomology of a conformally compact metric
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudokonvexen Gebieten
• On the Differential Form Spectrum of Negatively Curved Riemannian Manifolds
• $L^2 $ harmonic forms and a conjecture of Dodziuk-Singer

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