Imperial College London
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ProfessorDarrenCrowdy

Faculty of Natural Sciences, Department of Mathematics

Professor in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8587d.crowdy Website

 
 
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Location

 

735Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Green:2022:10.1098/rspa.2021.0832,
author = {Green, C and Snipes, M and Ward, L and Crowdy, D},
doi = {10.1098/rspa.2021.0832},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
pages = {1--20},
title = {Harmonic-measure distribution functions for a class of multiply connected symmetrical slit domains},
url = {http://dx.doi.org/10.1098/rspa.2021.0832},
volume = {478},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The harmonic-measure distribution function, or h-function, of a planar domain Ω⊂C with respect to a basepoint z0∈Ω is a signature that profiles the behaviour in Ω of a Brownian particle starting from z0. Explicit calculation of h-functions for a wide array of simply connected domains using conformal mapping techniques has allowed many rich connections to be made between the geometry of the domain and the behaviour of its h-function. Until now, almost all h-function computations have been confined to simply connected domains. In this work, we apply the theory of the Schottky–Klein prime function to explicitly compute the h-function of the doubly connected slit domain C([−1/2,−1/6]∪[1/6,1/2]). In view of the connection between the middle-thirds Cantor set and highly multiply connected symmetric slit domains, we then extend our methodology to explicitly construct the h-functions associated with symmetric slit domains of arbitrary even connectivity. To highlight both the versatility and generality of our results, we graph the h-functions associated with quadruply and octuply connected slit domains.
AU  - Green,C
AU  - Snipes,M
AU  - Ward,L
AU  - Crowdy,D
DO  - 10.1098/rspa.2021.0832
EP  - 20
PY  - 2022///
SN  - 1364-5021
SP  - 1
TI  - Harmonic-measure distribution functions for a class of multiply connected symmetrical slit domains
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2021.0832
UR  - https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0832#d5074953e1
UR  - http://hdl.handle.net/10044/1/96062
VL  - 478
ER  -
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