Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation | Zendy

Roth Oliver | Zendy; Schleißinger Sebastian | Zendy

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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.

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