Work

Extremal length and duality

Year: 2024

Type: article

Abstract: Classical extremal length (or conformal modulus) is a conformal invariant involving families of paths on the Riemann sphere. In “Extremal length and functional completion”, Fuglede initiated an abstract theory of extremal length which has since been widely applied. Concentrating on duality properties and applications to quasiconformal analysis, we demonstrate the flexibility of the theory and present recent advances in three different settings: (1) Extremal length and uniformization of metric surfaces. (2) Extremal length of families of surfaces and quasiconformal maps between n -dimensional spaces. (3) Schramm’s transboundary extremal length and conformal maps between multiply connected plane domains.

Source: Expositiones Mathematicae

DOI: 10.1016/j.exmath.2024.125634

Author: Kai Rajala

Institution: University of Jyväskylä

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funder: Academy of Finland