The \({\overline{\partial}}\) operator along the leaves and Guichard's theorem for a complex simple foliation

DOI10.1007/s00208-009-0459-9zbMath1209.32021OpenAlexW2461991598MaRDI QIDQ976778

Aziz El Kacimi Alaoui

Publication date: 16 June 2010

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-009-0459-9

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Deformations of complex structures (32G05) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items

On the cohomological equation of a linear contraction ⋮ On leafwise meromorphic functions with prescribed poles ⋮ \(\overline{\partial}\)-tangential invariants of certain vector bundles over complex foliations ⋮ Transversally pseudoconvex semiholomorphic foliations ⋮ Leafwise Dolbeault cohomology of certain complex foliations ⋮ $1$-complete semiholomorphic foliations

Cites Work

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• Riemann's mapping theorem for variable metrics
• Leafwise Dolbeault cohomology of certain complex foliations
• Sums of an entire function in certain weighted \(L^2\)-spaces
• On the parameter dependence of solutions to the \(\bar\partial\)-equation
• A smooth foliation of the 5-sphere by complex surfaces
• Cohomological equations of Riemannian flows and the Anosov diffeomorphism
• On Sobolev infinitesimal rigidity of linear hyperbolic actions on the 2-torus
• Foliated manifolds with bundle-like metrics
• Foliations with complex leaves

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