On the $L^2$-Dolbeault cohomology of annuli

Debraj Chakrabarti; Christine Laurent-Thiébaut; Mei-Chi Shaw

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arXiv · 1602.03896

On the $L^2$-Dolbeault cohomology of annuli

Debraj Chakrabarti·Christine Laurent-Thiébaut·Mei-Chi Shaw

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Abstract

For certain annuli in $\mathbb{C}^n$, $n\geq 2$, with non-smooth holes, we show that the $\bar{\partial}$-operator from $L^2$ functions to $L^2$ $(0,1)$-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 $W^1$ for the $\bar{\partial}$-equation on the non-smooth domains which are the holes of these annuli.

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BibTeX RIS

Debraj Chakrabarti, Christine Laurent-Thiébaut, Mei-Chi Shaw. 2016-02-11. On the $L^2$-Dolbeault cohomology of annuli. https://arxiv.org/abs/1602.03896

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