A Parameter Version of Forstnerič's Splitting Lemma

2018/02/05 by Simon, Lars · 1 citation
#32H02 (Primary) 32W05 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.01442

Abstract

We construct solution operators to the ∂-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.

Cited by

• The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces

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