Boundary behaviour of Loewner Chains
Alexander Kuznetsov (Saratov State University)
TL;DR
This paper investigates the boundary behavior of Loewner chains, establishing conditions under which their solutions map the unit disc to domains with specific boundary properties or extend analytically.
Contribution
It provides new criteria for the boundary regularity and extendability of solutions to the Loewner-Kufarev equation.
Findings
Conditions for quasiconformal rectifiable boundary mappings
Criteria for extension of solutions to closed unit disc
Results on inverse function continuation
Abstract
In paper found conditions that guarantee that solution of Loewner-Kufarev equation maps unit disc onto domain with quasiconformal rectifiable boundary, or it has continuation on closed unit disc, or it's inverse function has continuation on closure of domain.
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Taxonomy
TopicsAnalytic and geometric function theory · Advanced Mathematical Modeling in Engineering · Meromorphic and Entire Functions