A Parameter Version of Forstnerič's Splitting Lemma

Abstract

We construct solution operators to the $\overline{\partial }$-equation that depend continuously on the domain. This is applied to derive a parameter version of Forstnerič's splitting lemma: If both the maps and the domains they are defined on vary continuously with a parameter, then the maps obtained from Forstnerič's splitting will depend continuously on the parameter as well.

20 pages