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arXiv · 1410.6417

Random conformal welding for finitely connected regions

Shi-Yi Lan·Wang Zhou
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Abstract

Given a finitely connected region $Ω$ of the Riemann sphere whose complement consists of $m$ mutually disjoint closed disks $\bar{U}_j$, the random homeomorphism $h_j$ on the boundary component $\partial U_j$ is constructed using the exponential Gaussian free field. The existence and uniqueness of random conformal welding of $Ω$ with $h_j$ is established by investigating a non-uniformly elliptic Betrami equation with a random complex dilatation. This generalizes the result of Astala, Jones, Kupiainen and Saksman to multiply connected domains.

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Shi-Yi Lan, Wang Zhou. 2014-10-23. Random conformal welding for finitely connected regions. https://arxiv.org/abs/1410.6417

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