On the mean curvature of the periodic surfaces of revolution
by Katsuei Kenmotsu (Mathematical Institute, Tohoku University, Sendai, Japão)
A surface of revolution in the Euclidean space is determined by the mean curvature. In this talk, a necessary and sufficient condition for such a surface to be periodic is given in terms of the mean curvature. This extends the famous result by Delaunay (1841) for constant mean curvature surfaces of revolution. First, we discuss with two dimensional case, and then the higher dimensional case, separately.