%0 Journal Article
%T Asymptotic quantization for probability measures on Riemannian manifolds
%A Mikaela Iacobelli
%J Mathematics
%D 2014
%I arXiv
%X In this paper we study the quantization problem for probability measures on Riemannian manifolds. Under a suitable assumption on the growth at infinity of the measure we find asymptotic estimates for the quantization error, generalizing the results on $\mathbb{R}^d.$ Our growth assumption depends on the curvature of the manifold and reduces, in the flat case, to a moment condition. We also build an example showing that our hypothesis is sharp.
%U http://arxiv.org/abs/1412.4026v1