On smooth moduli space of Riemann surfaces

arXiv1610.03132MaRDI QIDQ6278487

Yong Hou

Publication date: 10 October 2016

Abstract: In this paper we study the smooth moduli space of closed Riemann surfaces. This smooth moduli is an infinite cover of the usual moduli space $mathscr{M}_g$ of closed Riemann surfaces, and is identified with the Schottky space of rank $g.$ The main theorem of the paper is: Closed Riemann surfaces are uniformizable by Schottky groups of Hausdorff dimension less than one. This work seem to be the only paper in literature to study question of Riemann surface uniformization and its Hausdorff dimension. We develop new techniques of rational norm of homological marking of Riemann surface and, decomposition of probability measures to prove our result. As an application of our theorem we have existence of period matrix of Riemann surface in coordinates of smooth moduli space.

Mathematics Subject Classification ID

Manifolds and cell complexes (57-XX) Differential geometry (53-XX)

This page was built for publication: On smooth moduli space of Riemann surfaces

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6278487)