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13 votes
2 answers
485 views

Geodesic current supported on a pencil?

Consider a geodesic current $\mu$ on a closed surface $\Sigma$, as defined by Bonahon ("The Geometry of Teichmüller space via geodesic currents"). These are $\pi_1(\Sigma)$-invariant measures on the ...
Dylan Thurston's user avatar
8 votes
2 answers
328 views

Equivalence of definitions of quasiconformal surfaces?

I have been reading John H. Hubbard's book Teichmüller Theory vol. 1 and I am a little bit concerned with his definition of quasiconformal surface. Definition: A quasiconformal surface $S$ is a ...
Maxime Scott's user avatar
8 votes
1 answer
600 views

Questions on Thurston's metric on Teichmüller space

I'm reading the famous "Minimal stretch maps between hyperbolic surfaces" by William Thurston and I'm trying to understand the key theorem 8.1. I have many unclear points so I hope someone can help me ...
Redin's user avatar
  • 81
3 votes
0 answers
198 views

Uniform continuity of length function on geodesic currents

I'm starting to study geodesic currents and I have a question concerning uniform continuity. Let's take $S$ a closed surface of genus $g$ and $GC(S)$ the space of geodesic currents on $S$ (as it is ...
user3419's user avatar