The Lowner-Kufarev representations for domains with analytic boundaries

Dmitri Prokhorov


We consider the Lowner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Lowner-Kufarev chain consisting of univalent quadratic polynomials and compare the Lowner-Kufarev representations of bounded and arbitrary univalent functions.


Lowner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions

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Date of publication: 2016-07-27 21:54:11
Date of submission: 2016-07-27 13:47:14


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