On the number of extremal surfaces

الأصل · EN

Let X be a compact Riemann surface of genus ≥ 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 extremal surface. This paper gives formulas enumerating extremal surfaces of genus ≥ 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.