On the length spectrum metric in infinite dimensional Teichmüller spaces

We consider the length spectrum metric d L in infinite dimensional Teichmller space T (R 0 ). It is known that d L defines the same topology as that of the Teichmller metric d T on T (R 0 ) if R 0 is a topologically finite Riemann surface. In 2003, Shiga proved that d L and d T define the same topology on T (R 0 ) if R 0 is a topologically infinite Riemann surface which can be decomposed into pairs of pants such that the lengths of all their boundary components except punctures are uniformly bounded by some positive constants from above and below. In this paper, we extend Shiga's result to Teichmller spaces of Riemann surfaces satisfying a certain geometric condition.