Abstract
Let be the unit disk and let be parametrizations of two slits such that and are disjoint.
Let be the unique normalized conformal mapping from onto with , . Furthermore, for , denote by the unique normalized conformal mapping from onto with , .
Loewner’s famous theorem (1923) can be stated in the following way: The function is differentiable at if and only if is differentiable at .
In this paper we compare the differentiability of with that of . We show that the situation is more complicated in the case with .
Furthermore, we also look at this problem in the case of a multiply connected domain with its corresponding Komatu–Loewner equation.
Funding Statement
The second author was partially supported by the ERC grant “HEVO–Holomorphic Evolution Equations” no. 277691.
Citation
Christoph Böhm. Sebastian Schleißinger. "The Loewner equation for multiple slits, multiply connected domains and branch points." Ark. Mat. 54 (2) 339 - 370, October 2016. https://doi.org/10.1007/s11512-016-0231-9
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