A note on the closed range of ∂¯ b on q-convex manifolds

Luca Baracco; Alexander Tumanov

doi:10.1007/s40627-020-00053-w

A note on the closed range of ∂¯ _b on q-convex manifolds

Luca Baracco, Alexander Tumanov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the tangential Cauchy–Riemann operator ∂¯ _b has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold X. Our result generalizes the known case when X is a Stein manifold (in particular, when X= Cⁿ).

Original language	English (US)
Article number	14
Journal	Complex Analysis and its Synergies
Volume	6
Issue number	2
DOIs	https://doi.org/10.1007/s40627-020-00053-w
State	Published - Jun 2020

Keywords

Closed Range
Analytic continuation
Boundary of Analytic sets

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Numerical Analysis

Online availability

10.1007/s40627-020-00053-w

Library availability

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Cite this

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title = "A note on the closed range of ∂¯ b on q-convex manifolds",

abstract = "We prove that the tangential Cauchy–Riemann operator ∂¯ b has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold X. Our result generalizes the known case when X is a Stein manifold (in particular, when X= Cn).",

keywords = "Closed Range, Analytic continuation, Boundary of Analytic sets",

author = "Luca Baracco and Alexander Tumanov",

note = "Funding Information: Research of the Alexander Tumanov is partially supported by Simons Foundation Grant. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

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KW - Analytic continuation

KW - Boundary of Analytic sets

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