On the number of extremal surfaces
Abstract
Description
Let $X$ be a compact Riemann surface of genus $\geq 2$ of constant negative curvature -1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an {\em extremal surface}.
This paper gives formulas enumerating extremal surfaces of genus $\geq 4$ up to isometry. We show also that the isometry group of an extremal surface is always cyclic of order 1, 2, 3 or 6.
14 pages, 1 figure
14 pages, 1 figure