Convex dynamics in Hele-Shaw cells.
The Löwner-Kufarev representations for domains with analytic boundaries
We consider the Löwner-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 Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions....
The Lowner-Kufarev representations for domains with analytic boundaries
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....
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