Premium
Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation
Author(s) -
Roth Oliver,
Schleißinger Sebastian
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdu054
Subject(s) - mathematics , unit disk , lemma (botany) , bounded function , univalent function , mathematical analysis , plane (geometry) , unit (ring theory) , pure mathematics , combinatorics , analytic function , geometry , ecology , poaceae , biology , mathematics education
We describe the region V ( z 0 ) of values of f ( z 0 ) for all normalized bounded univalent functions f in the unit disk D at a fixed pointz 0 ∈ D . The proof is based on the radial Loewner differential equation. We also prove an analogous result for the upper half‐plane using the chordal Loewner equation.