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

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

For certain annuli in ${\mathbb{C}}^n$, $n\ge 2$, 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…