The global structure of constant mean curvature surfaces
Let MC1 denote a complete, finite topology, properly embedded surface with constant mean curvature 1. Kapouleas constructed a wealth of MC1 surfaces by starting with a linear graph in \(\mathbb{R}^ 3\) satisfying a balancing condition at each vertex. The present authors prove global properties of MC1 surfaces giving partial answers to a conjecture that all MC1 surfaces ``look like Kapouleas examples'' in some sense. In particular they use a force and torque vector assigned invariantly to each homology class of 1-cycles on an MC1 surface.
scientific article; zbMATH DE number 549652
scientific article