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Univalent Functions
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-017-0205-3
- Publisher site
- See Article on Publisher Site
Abstract
In this note, we consider a multi-slit Loewner equation with constant coefficients that describes the growth of multiple SLE curves connecting N points on $$\mathbb {R}$$ R to infinity within the upper half-plane. For every $$N\in \mathbb {N}$$ N ∈ N , this equation yields a measure-valued process $$t\mapsto \{\alpha _{N,t}\},$$ t ↦ { α N , t } , and we are interested in the limit behaviour as $$N\rightarrow \infty .$$ N → ∞ . We prove tightness of the sequence $$\{\alpha _{N,t}\}_{N\in \mathbb {N}}$$ { α N , t } N ∈ N under certain assumptions and address some further problems. Moreover, we investigate a similar situation in which all slits are trajectories of a certain quadratic differential.
Journal
Computational Methods and Function Theory – Springer Journals
Published: May 25, 2017