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

preprint2012arXivOpen access

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 $\C^N$.

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

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