Physical Sciences and Mathematics Commons^™

The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg

Robert Kusner

This paper develops new tools for understanding surfaces with more than one end and infinite topology which are properly minimally embedded in Euclidean three-space. On such a surface, the set of ends forms a totally disconnected compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies that the surface can have at most two limit ends, which occur at the top and bottom of the ordering, and thus only a countable …