Asymptotic quantization for probability measures on Riemannian manifolds
Mikaela Iacobelli · ESAIM Control Optimisation and Calculus of Variations · 2015
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 Rd. 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.