Extremal disks and extremal surfaces of genus three
Nakamura, Gou
Kodai Math. J., Tome 28 (2005) no. 1, p. 111-130 / Harvested from Project Euclid
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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.
Publié le : 2005-03-14
Classification:  
@article{1111588041,
     author = {Nakamura, Gou},
     title = {Extremal disks and extremal surfaces of genus three},
     journal = {Kodai Math. J.},
     volume = {28},
     number = {1},
     year = {2005},
     pages = { 111-130},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1111588041}
}

Nakamura, Gou. Extremal disks and extremal surfaces of genus three. Kodai Math. J., Tome 28 (2005) no. 1, pp.  111-130. http://gdmltest.u-ga.fr/item/1111588041/