We define two pseudo-metrics L_F and K_F on the Teichmüller space of semi-translation surfaces, which are the symmetric counterparts to the metrics defined by William Thurston. We prove some nice properties of L_F and K_F, most notably that they are complete pseudo-metrics. In the second part of the thesis we define their asymmetric analogues L_F^a and K_F^a and prove that their equality depends on two statements regarding 1-Lipschitz maps between polygons. We are able to prove the first statement, but the second one remains a conjecture: nonetheless, we explain why we believe it is true.
Thurston's metric on Teichmüller space of semi-translation surfaces / Wolenski, Federico. - (2018 Sep 14).
Thurston's metric on Teichmüller space of semi-translation surfaces
WOLENSKI, FEDERICO
14/09/2018
Abstract
We define two pseudo-metrics L_F and K_F on the Teichmüller space of semi-translation surfaces, which are the symmetric counterparts to the metrics defined by William Thurston. We prove some nice properties of L_F and K_F, most notably that they are complete pseudo-metrics. In the second part of the thesis we define their asymmetric analogues L_F^a and K_F^a and prove that their equality depends on two statements regarding 1-Lipschitz maps between polygons. We are able to prove the first statement, but the second one remains a conjecture: nonetheless, we explain why we believe it is true.File | Dimensione | Formato | |
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Tesi_dottorato_Wolenski.pdf
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