부산대학교 도서관

In this paper, the authors classify polynomial minimal surfaces of degree five and lower up to similarities and linear reparametrisations: the cubic Enneper surface, a family of quartic surfaces, and three families of quintic surfaces. The paper points out the relation between minimal surfaces and Pythagorean hodograph (PH) curves. In particular, the Weierstrass formula allows a bijective mapping between planar PH curves and polynomial minimal surfaces up to similarities and linear reparametrisations. A planar PH curve is one of the isoparametric curves of any polynomial minimal surface.