A gradient flow perspective on the quantization problem

Abstract

In this paper we review recent results by the author on the problem of quantization of measures. More precisely, we propose a dynamical approach, and we investigate it in dimensions 1 and 2. Moreover, we discuss a recent general result on the static problem on arbitrary Riemannian manifolds.

17 pages, 7 figures, proceedings for the Indam Workshop "PDE models for multi-agent phenomena" held in Rome, Italy, 28 November - 2 December 2016