The topological types of length bounded multicurves

Abstract

This article discusses inequalities on lengths of curves on hyperbolic surfaces. In particular, a characterization is given of which topological types of curves and multicurves always have a representative that satisfies a length inequality that holds over all of moduli space.

arXiv commentThe final version of this article will appear in the book "Essays in Geometry, dedicated to Norbert A'Campo" (A. Papadopoulos, ed.), European Mathematical Society Press, Berlin, 2022 (to appear)