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Title:
Parabolicity and Fenchel Nielsen Coordinates
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Abstract:
Fix a topological pants decomposition P of an infinite surface X. The set of conformal hyperbolic metrics on X is parametrized by the Fenchel-Nielsen coordinates on the pants decomposition P. We give sufficient conditions on the Fenchel-Nielsen coordinates such that the harmonic type of X is parabolic, i.e. X does not support a Green's function. Our main techniques are modulus estimated for degenerating families of curves. These estimates allow us to determine the asymptotics of the modulus of the so-called non-standard collar about a hyperbolic geodesic and give new criteria for parabolicity. This is joint work with Ara Basmajian and Dragomir Saric.
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