Structure theorem for CMC surfaces embedded in R^3 with locally bounded genus

Author: William Meeks

Abstract: Fix \(R>0\). We derive a local structure theorem for the space \(\mathcal{M}(R)\) of connected compact CMC = 1 surfaces \(M\) of genus 0 properly embedded in the open ball \(B(R)\) of radius \(R>0\). This structure theorem has interesting applications that I will also discuss, including the compactness of the space \(\mathcal{M}(R)\).