Dimensionality of Local Minimizers of the Interaction Energy

TL;DR

This paper investigates how the dimensionality of local energy minimizers in a repulsive-attractive potential system depends on the potential's strength at the origin, providing insights into the structure of these minimizers.

Contribution

It establishes a relationship between the support's dimensionality of local minimizers and the repulsive strength of the potential at zero, advancing understanding of energy landscape structures.

Findings

Support dimensionality linked to repulsive strength at origin

Characterization of local minimizers in transport topology

Insights into energy minimization structures

Abstract

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.