A Historical Survey of Quasiconformal Mappings

Olli Lehto
Additional contact information
Olli Lehto: University of Helsinki, Department of Mathematics

A chapter in Zum Werk Leonhard Eulers, 1984, pp 205-217 from Springer

Abstract: Abstract By the classical definition, a quasiconformal mapping is a sense-preserving diffeomorphism of a plane domain onto another plane domain which maps infinitesimal circles onto infinitesimal ellipses with a uniformly bounded ratio of axes. Later it was found preferable to relax a priori differentiability conditions and define a quasiconformal mapping in the plane as a sense-preserving homeomorphism which leaves some conformai invariant quasi — invariant. The most general conformai invariant suitable for this purpose is the module of a path family. The precise requirement for quasiconfrormality is the existence of a fixed constant K such that the module of every path family lying in the domain in which the homeomorphism is considered increases at most K times.

Date: 1984
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:978-3-0348-7121-1_12

Ordering information: This item can be ordered from
http://www.springer.com/9783034871211

DOI: 10.1007/978-3-0348-7121-1_12

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 ().