Before revision:  In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold M^h using information from a given point cloud that was developed by Sober \& Levin in 2019 . They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary .
After revision:  In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold M^h using information from a given point cloud that was developed by Sober \& Levin in 2019. In this paper, we show that provided that M\in C^{k} is closed , i.e. M is a compact manifold without boundary .