Optimal constants of $L^2$ inequalities for closed nearly umbilical hypersurfaces in space forms

Xu Cheng, Areli Vázquez Juárez

Let $\Sigma$ be a smooth closed hypersurface with non-negative Ricci curvature, isometrically immersed in a space form. It has been proved in \cite{P}, \cite{CZ}, and \cite{C2} that the…