Solving the Loewner PDE in complete hyperbolic starlike domains of $\C^N$

Abstract

We prove that any Loewner PDE in a complete hyperbolic starlike domain of $\C^N$ (in particular in bounded convex domains) admits an essentially unique univalent solution with values in $\C^N$.

8 pages

References in corpus (3)

• Resonances in Loewner equations
• Evolution Families and the Loewner Equation I: The Unit Disc
• Local duality in Loewner equations