II Currents and complex structures

Christine Laurent-Thiébaut ()
Additional contact information
Christine Laurent-Thiébaut: Université Joseph Fourier, Institut Fourier

A chapter in Holomorphic Function Theory in Several Variables, 2011, pp 21-55 from Springer

Abstract: Abstract In this chapter we introduce two new ideas, one coming from differential geometry (currents) and the other coming from analysis (complex analytic manifolds and their associated complex structures), which we will use frequently throughout the rest of this book. We start by defining currents, which for differential forms play the role that distributions play for functions, and then consider the regularisation problem for currents defined on a C∞ differential manifold. Solving this problem, which is easy in $$\mathbb{R}^{n}$$ by means of convolution, obliges us to introduce kernels with similar properties to the convolution kernel. We will also study the Kronecker index of two currents, which generalises the pairing of a current and a differential form. This index enables us to prove a fairly general Stokes’ formula which will be used in Chapters III and IV.

Keywords: Erential Form; Strong Topology; Integration Current; Singular Support; Dolbeault Cohomology (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-030-4_2

Ordering information: This item can be ordered from
http://www.springer.com/9780857290304

DOI: 10.1007/978-0-85729-030-4_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().