Flat points of minimal balance surfaces

Abstract

The symmetry conditions for flat points of minimal surfaces have been studied in relation to the order β of points on such surfaces. Using symmetry aspects, a set of rules for the derivation of fiat points have been developed. By means of these rules the flat points for the 45 families of minimal balance surfaces known so far have been determined. As a check for completeness the relation between the genus of a minimal surface and the orders of its flat points has been used.