Advertisement

Differential Forms and Dolbeault Theory

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 236)

Abstract

In this chapter Dolbeault cohomology theory is presented. One of the basic tools is the \(\bar \partial \)-integration lemma for closed (p, q)-forms (Theorem 4.1). The proof of this lemma is based on the existence of bounded solutions of the inhomogeneous Cauchy-Riemann differential equation \(\partial g/\partial \bar z = f.\)This solution is constructed in Paragraph 3 by means of the classical integral operator
$$Tf(z,u) = \frac{1}{{2\pi i}}\iint\limits_B {\frac{{f(\zeta ,u)}}{{\zeta - z}}}d\zeta \wedge d\bar \zeta .$$

Keywords

Tangent Vector Differential Form Complex Manifold Differentiable Manifold Stein Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenFederal Republic of Germany
  2. 2.Mathematisches InstitutWestfälischen Wilhelms-UniversitätMünsterFederal Republic of Germany

Personalised recommendations