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 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
@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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