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 $\mathcal{M}(R)$.