4,067 research outputs found
Holomorphic evolution: metamorphosis of the Loewner equation
This is a survey on recent results on the Loewner theory in one and several
complex manifoldsComment: 26 page
Simultaneous models for commuting holomorphic self-maps of the ball
We prove that a finite family of commuting holomorphic self-maps of the unit
ball admits a simultaneous holomorphic
conjugacy to a family of commuting automorphisms of a possibly lower
dimensional ball, and that such conjugacy satisfies a universal property. As an
application we describe when a hyperbolic and a parabolic holomorphic self-map
of can commute.Comment: Final version, to appear on Adv. Mat
Support points and the Bieberbach conjecture in higher dimension
We describe some open questions related to support points in the class
and introduce some useful techniques toward a higher dimensional Bieberbach
conjecture
- β¦