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Abstract
In this note we discuss some problems related to conformal slit-mappings. On the one hand, classical Loewner theory leads us to questions concerning the embedding of univalent functions into slit-like Loewner chains. On the other hand, a recent result from monotone probability theory motivates the study of univalent functions from a probabilistic perspective.
Acknowledgments
The authors would like to thank Mihai Iancu for helpful discussions and the proof of Theorem 2.2.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The first author was supported by JSPS KAKENHI Grant no. 17K14205. The second author was supported by the German Research Foundation (DFG), project no. 401281084.