SOME REMARKS ON THURSTON METRIC AND HYPERBOLIC METRIC

Title & Authors
SOME REMARKS ON THURSTON METRIC AND HYPERBOLIC METRIC
Sun, Zongliang;

Abstract
In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $\small{g{\geq}2}$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $\small{Teichm{\ddot{u}}ller}$ metric, the length spectrum metric and Thurston`s asymmetric metrics.
Keywords
complex projective structure;hyperbolic metric;marked length spectrum;$\small{Teichm{\ddot{u}}ller}$ space;Thurston metric;
Language
English
Cited by
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