Almost-isometry between the Teichmuller metric and the arc-length-spectrum metric on moduli space for surfaces with boundary

摘要

We show that the Teichmilller metric and the arc-length-spectrum metric are almost isometric, but they are not almost-isometric to the length-spectrum metric, on the moduli space of surfaces with non-empty boundary. (C) 2017 Elsevier B.V. All rights reserved.