Year: 2024
Type: article
Abstract: In this paper we present explicit solutions to the radial and chordal Loewner PDEs and we make an extensive study of their geometry. Specifically, we study multi-slit Loewner flows, driven by the time-dependent point masses $$\mu _{t}:=\sum _{j=1}^{n}b_j \delta _{\{\zeta _j e^{iat}\}}$$ μ t : = ∑ j = 1 n b j δ { ζ j e iat } in the radial case and $$\nu _t:=\sum _{j=1}^{n}b_j\delta _{\{k_j\sqrt{1-t}\}}$$ ν t : = ∑ j = 1 n b j δ { k j 1 - t } in the chordal case, where all the above parameters are chosen arbitrarily. Furthermore, we investigate their close connection to the semigroup theory of holomorphic functions, which also allows us to map the chordal case to the radial one.
Author: E. K. Theodosiadis
Institution: Stockholm University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Stockholms Universitet
OpenAlex ID: W4403378067