Asymptotic quantization for probability measures on Riemannian manifolds
1 University of Rome Sapienza, Department of Mathematics Guido
Castelnuovo, Piazzale Aldo Moro 5, 00185 Rome, Italy.
2 Ecole Polytechnique, Centre de mathématiques Laurent Schwartz, 91128 Palaiseau cedex, France.
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.
Mathematics Subject Classification: 49Q20
Key words: Quantization of measures / Riemannian manifolds
© EDP Sciences, SMAI 2016