  The Laplace-Beltrami operator (LBO) is a fundamental object associated to
Riemannian manifolds, which encodes all intrinsic geometry of the manifolds and
has many desirable properties. Recently, we proposed a novel numerical method,
Point Integral method (PIM), to discretize the Laplace-Beltrami operator on
point clouds \cite{LSS}. In this paper, we analyze the convergence of Point
Integral method (PIM) for Poisson equation with Neumann boundary condition on
submanifolds isometrically embedded in Euclidean spaces.
