A gradient flow perspective on the quantization problem

TL;DR

This paper reviews a dynamical approach to measure quantization, analyzing recent results in low dimensions and extending static quantization problems to Riemannian manifolds, offering new insights into the mathematical structure of quantization.

Contribution

It introduces a gradient flow perspective on measure quantization and extends the analysis to arbitrary Riemannian manifolds, providing a unified dynamical framework.

Findings

Analysis of quantization in 1 and 2 dimensions

Extension of static quantization results to Riemannian manifolds

New dynamical approach to measure quantization

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.