A sharp Schwarz inequality on the boundary

Details A sharp Schwarz inequality on the boundary A sharp Schwarz inequality on the boundary

1997-12-22

arxiv.org/abs/math/9712280v1

Mathematics

Complex Variables

Scientific paper

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 $b$ maps to the boundary, then the map is a magnification at $b$. 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 $b$ unless it is a rotation.

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