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- W2024140211 abstract "It has been shown that univalent circle packings filling in the complex plane $bold C$ are unique up to similarities of $bold C$. Here we prove that bounded degree branched circle packings properly covering $bold C$ are uniquely determined, up to similarities of $bold C$, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result. We also establish a circle packing analogue of Liouville's theorem: if $f$ is a circle packing map whose domain packing is infinite, univalent, and has recurrent tangency graph, then the ratio map associated with $f$ is either unbounded or constant." @default.
- W2024140211 created "2016-06-24" @default.
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- W2024140211 date "1995-05-10" @default.
- W2024140211 modified "2023-09-27" @default.
- W2024140211 title "Recurrent random walks, Liouville's theorem, and circle packings" @default.
- W2024140211 hasPublicationYear "1995" @default.
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