Corrections to "Extremal disks and extremal surfaces of genus three"

Abstract

We correct a result in "Extremal disks and extremal surfaces of genus three", Kodai Math. J. 28, no. 1 (2005), 111-130. In the paper we have shown that there exist 16 compact Riemann surfaces of genus three up to conformal equivalence in which two extremal disks are isometrically embedded. However we have three more of them up to conformal equivalence. In the present paper we give these three surfaces and show that they are hyperelliptic. We also determine the groups of automorphisms of them.