LOWER BOUNDS OF LIPSCHITZ CONSTANTS TO CURVE COMPLEXES OF PUNCTURED RIEMANN SURFACES
Let be a closed Riemann surface of genus Gadre et al. [4] showed that the optimal Lipschitz constant for a systol map from the Teichmüller space to the curve complex behaves like for sufficiently large p. For Riemann surfaces with punctures, Aougab-Taylor showed that there exists a uniform constant L such that for any Riemann surface of type In this paper, we show that
As a consequence, we also prove that the constant L can be chosen to satisfy
Riemann surfaces, pseudo-Anosov, Dehn twists, curve complex, filling curves.