Kodai Mathematical Journal

Extremal disks and extremal surfaces of genus three

Gou Nakamura

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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.

Article information

Source
Kodai Math. J. Volume 28, Number 1 (2005), 111-130.

Dates
First available in Project Euclid: 23 March 2005

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1111588041

Digital Object Identifier
doi:10.2996/kmj/1111588041

Mathematical Reviews number (MathSciNet)
MR2122195

Zentralblatt MATH identifier
1088.30038

Citation

Nakamura, Gou. Extremal disks and extremal surfaces of genus three. Kodai Math. J. 28 (2005), no. 1, 111--130. doi:10.2996/kmj/1111588041. http://projecteuclid.org/euclid.kmj/1111588041.


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