Shearing process and an example of a bounded support function in $S^0({\mathbb{B}}^2)$

Abstract

We introduce a process, that we call "shearing", which for any given normal Loewner chain produces a normal Loewner chain made of shears automorphisms. As an application, and in stringent contrast to the one-dimensional case, we prove the existence of a starlike bounded function in the class $S^0$ of the ball ${\mathbb{B}}^2$ (in fact the restriction of a shear automorphism of ${\mathbb{C}}^2$) which is a support point for a linear continuous functional.

Cited by in corpus (1)

• Variation of Loewner chains, extreme and support points in the class $S^0$ in higher dimensions