EARTHQUAKES IN THE LENGTH-SPECTRUM TEICHMÜLLER SPACES.

Let X0 be a complete hyperbolic surface of infinite type that has a geodesic pants decomposition with cuff lengths bounded above. The length spectrum Teichmüller space Tls(X0) consists of homotopy classes of hyperbolic metrics on X0 such that the ratios of the corresponding simple closed geodesic for the hyperbolic metric on X0 and for the other hyperbolic metric are bounded from below away from 0 and from above away from ∞;. This paper studies earthquakes in the length spectrum Teichmüller space Tls(X0). We find a necessary condition and several sufficient conditions on the earthquake measure μ such that the corresponding earthquake Eμ describes a hyperbolic metric on X0 which is in the length spectrum Teichmüller space. Moreover, we give examples of earthquake paths t → Etμ, for t ≥ 0, such that Etμ ∈ Tls(X0) for 0 ≤ t < t0, Et0μ/∉ Tls(X0) and Etμ ∈ Tls(X0) for t > t0. [ABSTRACT FROM AUTHOR]