volume 26, issue 3, P321-351 2001
DOI: 10.1007/s00454-001-0040-0
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Abstract: The fat flow modulus is a discrete version of the classical conformal modulus; one can use it to classify triangulations of half-open annuli as parabolic or hyperbolic. There exist various criteria for parabolicity; several of these criteria involve the vertex valences of the triangulation. In this paper we decompose the half-open annulus into a family of concentric sub-annuli. We can estimate the fat flow moduli of these sub-annuli in terms of their vertex valences. By using the Layer Theorem of Cannon et al…

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