Remarks on the boundary curve of a constant mean curvature topological disc. Issue 8 (3rd August 2017) - Brander, David; Lopéz, Rafael
Abstract : We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the boundary curve, and a condition for the surface to be totally umbilic in terms of the normal curvature.