Abstract
A compact Riemann surface of genus g ≥ 2 is said to be extremal if it admits an extremal disk, a disk of the maximal radius determined by g. If g = 2 or g ≥ 4, it is known that how many extremal disks an extremal surface of genus g can admit. In the present paper we deal with the case of g = 3. Considering the side-pairing patterns of the fundamental polygons, we show that extremal surfaces of genus 3 admit at most two extremal disks and that 16 surfaces admit exactly two. Also we describe the group of automorphisms and hyperelliptic surfaces.
Citation
Gou Nakamura. "Extremal disks and extremal surfaces of genus three." Kodai Math. J. 28 (1) 111 - 130, March 2005. https://doi.org/10.2996/kmj/1111588041
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