On the L²-Dolbeault cohomology of annuli

2016/02/11 by Chakrabarti, Debraj, Laurent-Thiébaut, Christine, Shaw, Mei-Chi · 1 citation
#32W05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.03896

Abstract

For certain annuli in ℂⁿ, n≥ 2, with non-smooth holes, we show that the ∂-operator from L² functions to L² (0,1)-forms has closed range. The holes admitted include products of pseudoconvex domains and certain intersections of smoothly bounded pseudoconvex domains. As a consequence, we obtain estimates in the Sobolev space W¹ for the ∂-equation on the non-smooth domains which are the holes of these annuli.

Cited by

• L²-Sobolev Theory for ∂ on Domains in \Bbb CPⁿ

Related

• A Modified Morrey-Kohn-Hörmander Identity and Applications
• Exact sequences and estimates for the ∂-problem
• L²-Sobolev Theory for ∂ on Domains in \Bbb CPⁿ
• Hearing pseudoconvexity in Lipschitz domains with holes via ∂
• The L²-cohomology of a bounded smooth Stein Domain is not necessarily Hausdorff