A characterization of Delaunay surfaces using a one-parameter family of touching spheres
The Delaunay surface is a surface of revolution with constant mean curvature in Euclidean 3-space. The Delaunay surface satisfies the property that there is a one-parameter family of spheres such that it meets each sphere tangentially along the intersection curve. One may ask whether the converse is true or not. In this talk, we give an affirmative answer to this question. This is joint work with Sung-Hong Min.