A sharp Schwarz inequality on the boundary
Complex Variables
2016-09-07 v1
Abstract
A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself taking the origin into the origin, and if some boundary point maps to the boundary, then the map is a magnification at . We prove a sharp quantitative version of this result which also sharpens a classical result of Loewner, and which implies that the map is a strict magnification at unless it is a rotation.
Keywords
Cite
@article{arxiv.math/9712280,
title = {A sharp Schwarz inequality on the boundary},
author = {Robert Osserman},
journal= {arXiv preprint arXiv:math/9712280},
year = {2016}
}