A Parametric Version of Forstnerič’s Splitting Lemma

  • Lars SimonEmail author


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


Compositional splitting Biholomorphic map Parameter dependence 

Mathematics Subject Classification

Primary 32H02 Secondary 32W05 


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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