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dc.contributor.authorGreen, Christopher C.
dc.contributor.authorSnipes, Marie A.
dc.contributor.authorWard, Lesley A.
dc.contributor.authorCrowdy, Darren G.
dc.identifier.citationGreen Christopher C., Snipes Marie A., Ward Lesley A. and Crowdy Darren G. 2022Harmonic-measure distribution functions for a class of multiply connected symmetrical slit domains Proc. R. Soc. A.4782021083220210832
dc.descriptionClick on the DOI to access this article (may not be free).en_US
dc.description.abstractThe 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.en_US
dc.publisherRoyal Societyen_US
dc.relation.ispartofseriesProceedings of the Royal Society;Volume 478 Issue 2259
dc.subjectConformal mapen_US
dc.subjectPrime functionen_US
dc.subjectMultiply connected slit domainen_US
dc.subjectHarmonic-measure distribution functionen_US
dc.titleHarmonic-measure distribution functions for a class of multiply connected symmetrical slit domainsen_US
dc.rights.holder© 2022 The Author(s)en_US

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