68 research outputs found
A characterization of short curves of a Teichmueller geodesic
We provide a combinatorial condition characterizing curves that are short
along a Teichmueller geodesic. This condition is closely related to the
condition provided by Minsky for curves in a hyperbolic 3-manifold to be short.
We show that short curves in a hyperbolic manifold homeomorphic to S x R are
also short in the corresponding Teichmueller geodesic, and we provide examples
demonstrating that the converse is not true.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper5.abs.htm
Length of a curve is quasi-convex along a Teichmuller geodesic
We show that for every simple closed curve \alpha, the extremal length and
the hyperbolic length of \alpha are quasi-convex functions along any
Teichmuller geodesic. As a corollary, we conclude that, in Teichmuller space
equipped with the Teichmuller metric, balls are quasi- convex.Comment: 25 pages, 2 figure
Uniform growth rate
In an evolutionary system in which the rules of mutation are local in nature,
the number of possible outcomes after mutations is an exponential function
of but with a rate that depends only on the set of rules and not the size
of the original object. We apply this principle to find a uniform upper bound
for the growth rate of certain groups including the mapping class group. We
also find a uniform upper bound for the growth rate of the number of homotopy
classes of triangulations of an oriented surface that can be obtained from a
given triangulation using diagonal flips.Comment: 13 pages, 5 figures, minor revisions, final version appears in Proc.
Amer. Math. So
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