Sharp Estimates for the Optimal Matching Problem on the 2-Torus

TL;DR

This paper provides precise estimates for the average cost of optimal matching on the 2-torus, employing linearization and trajectory methods to improve understanding of geometric matching problems.

Contribution

It introduces sharp bounds for the optimal matching problem on the 2-torus, advancing theoretical understanding with novel analytical techniques.

Findings

Sharp estimates for average matching cost derived

Quantitative linearization applied to geometric matching

Method of trajectories used for improved bounds

Abstract

In this paper, we prove sharp estimates for the average cost of the optimal matching problem on the flat 2-torus, using quantitative linearization and the method of trajectories.