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
• Enlaces
  • Texto completo
• 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