Asymptotic quantization for probability measures on Riemannian manifolds

摘要

In this paper we study the quantization problem for probability measures onRiemannian manifolds. Under a suitable assumption on the growth at infinity ofthe measure we find asymptotic estimates for the quantization error,generalizing the results on $\mathbb{R}^d.$ Our growth assumption depends onthe curvature of the manifold and reduces, in the flat case, to a momentcondition. We also build an example showing that our hypothesis is sharp.