1997/12/22 by Robert Osserman, Osserman, Robert · 2 citations
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.math/9712280
openalex publication_date 1997/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.