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Results tagged with hyperbolic-geometry
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user 5010
6
votes
Converse to Wolpert's Lemma
The answer is no, but it's actually a deep question and leads to another metric on the Teichmüller space of surfaces. The minimum quasi-conformal constant of a map in a given homotopy class is the Tei …
- 10.1k
6
votes
Tiling of genus 2 surface by 8 pentagons
Ian answered the second question as asked, but in case you meant to ask a different question: there is not always a symmetric tiling by regular polygons of the given type, even if those restrictions h …
- 10.1k
13
votes
2
answers
482
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 s …
- 10.1k
3
votes
teichmuller geodesics and hyperbolic mapping torus
To expand on Lee's answer, recall that Teichmüller space can be divided up into a "thin part" (where some geodesic is short, or equivalently where some conformal annulus has large modulus), and its co …
- 10.1k
3
votes
Accepted
Conformal invariants of planar pairs of pants
There are several references that consider the relation between extremal length and hyperbolic length. Usually they consider closed surfaces, but you can put yourself in that situation by doubling alo …
- 10.1k