On the L²-Dolbeault cohomology of annuli

2016/02/11 by Debraj Chakrabarti, Chakrabarti, Debraj, Christine Laurent-Thiébaut +3 · 1 citation
Mathematics · #32W05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32W05

paper · pdf · doi:10.48550/arxiv.1602.03896

Small typos corrected; Final Version; To appear in Indiana University Mathematics Journal

arxiv created 2016/08/03 · arxiv updated 2016/08/04

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.

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