Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology
arXiv:2012.00956 · doi:10.1007/s10711-025-00982-y
Abstract
We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the graphical sense away from a finite set of points. This is a CMC version of a result for minimal surfaces by Fraser-Li \cite{fraser.a-li.m2014}.
29 pages, 8 figures, main result extended to more general statement with updated proof. This version contains the corrected pictures that we improperly rendered on journal version