Univalence and holomorphic extension of the solution to $\omega$-controlled Loewner-Kufarev equations

Abstract

We prove that a solution to the $\omega$-controlled Loewner-Kufarev equation, which was introduced by the first two authors, exists uniquely, is univalent and starlike on the unit disk and can be extended holomorphically across the unit circle.

In this second version, Lemma 3.3 and the starlikeness in Theorems 1.1 and 3.5 are added for the sake of completeness