Advertisement

A Parametric Version of Forstnerič’s Splitting Lemma

  • Lars Simon
Article
  • 16 Downloads

Abstract

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.

Keywords

Compositional splitting Biholomorphic map Parameter dependence 

Mathematics Subject Classification

Primary 32H02 Secondary 32W05 

References

  1. 1.
    Deng, F., Fornaess, J.E., Fornaess Wold, E.: Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces. ArXiv e-prints. arXiv:1607.02755 (2016)
  2. 2.
    Diederich, K., Fornæss, J.E., Wold, E.F.: Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type. J. Geom. Anal. 24(4), 2124–2134 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Forstneriĉ, F.: Noncritical holomorphic functions on Stein manifolds. Acta Math. 191(2), 143–189 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Forstneriĉ, F.: Stein Manifolds and Holomorphic Mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 56. Springer, Berlin (2011)CrossRefGoogle Scholar
  5. 5.
    Forstneriĉ, F.: Stein manifolds and holomorphic mappings, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 56, Springer, Cham (2017) (The homotopy principle in complex analysis)Google Scholar
  6. 6.
    Range, R.M.: Holomorphic Functions and Integral Representations in Several Complex Variables. Springer, New York (1986)CrossRefzbMATHGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

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

Personalised recommendations