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 - 2020

Keywords

Closed Range
Analytic continuation
Boundary of Analytic sets

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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).",

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AU - Tumanov, Alexander

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AB - 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).

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KW - Analytic continuation

KW - Boundary of Analytic sets

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DO - 10.1007/s40627-020-00053-w

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VL - 6

JO - Complex Analysis and its Synergies

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SN - 2524-7581

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