Kodai Mathematical Journal
- Kodai Math. J.
- Volume 28, Number 1 (2005), 111-130.
Extremal disks and extremal surfaces of genus three
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.
Kodai Math. J. Volume 28, Number 1 (2005), 111-130.
First available in Project Euclid: 23 March 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Nakamura, Gou. Extremal disks and extremal surfaces of genus three. Kodai Math. J. 28 (2005), no. 1, 111--130. doi:10.2996/kmj/1111588041. https://projecteuclid.org/euclid.kmj/1111588041.