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 ${R}^{d}.$ 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.

DOI: 10.1051/cocv/2015025

Keywords: Quantization of measures, Riemannian manifolds

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@article{COCV_2016__22_3_770_0, author = {Iacobelli, Mikaela}, title = {Asymptotic quantization for probability measures on {Riemannian} manifolds}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {770--785}, publisher = {EDP-Sciences}, volume = {22}, number = {3}, year = {2016}, doi = {10.1051/cocv/2015025}, zbl = {1344.49074}, mrnumber = {3527943}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2015025/} }

TY - JOUR AU - Iacobelli, Mikaela TI - Asymptotic quantization for probability measures on Riemannian manifolds JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 770 EP - 785 VL - 22 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015025/ DO - 10.1051/cocv/2015025 LA - en ID - COCV_2016__22_3_770_0 ER -

%0 Journal Article %A Iacobelli, Mikaela %T Asymptotic quantization for probability measures on Riemannian manifolds %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 770-785 %V 22 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015025/ %R 10.1051/cocv/2015025 %G en %F COCV_2016__22_3_770_0

Iacobelli, Mikaela. Asymptotic quantization for probability measures on Riemannian manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 3, pp. 770-785. doi : 10.1051/cocv/2015025. http://archive.numdam.org/articles/10.1051/cocv/2015025/

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