Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation
- Autores: Oliver Roth, Sebastian Schleibinger
- Localización: Bulletin of the London Mathematical Society, ISSN 0024-6093, Vol. 46, Nº 5, 2014, págs. 1099-1109
- Idioma: inglés
- DOI: 10.1112/blms/bdu054
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Resumen
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 point z 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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