On the number of extremal surfaces

Details On the number of extremal surfaces On the number of extremal surfaces

2003-11-28

arxiv.org/abs/math/0311533v1

Mathematics

Differential Geometry

14 pages, 1 figure

Scientific paper

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.

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