The size of the singular set of area-minimizing currents

TL;DR

This survey reviews recent advances in understanding the regularity and singular set size of area-minimizing currents in higher codimension, highlighting new theoretical insights and methods.

Contribution

It compiles and discusses recent results on the structure and size of singular sets in higher codimension area-minimizing currents, advancing the theoretical understanding.

Findings

Characterization of the singular set size

New regularity results in higher codimension

Enhanced techniques for analyzing area-minimizing currents

Abstract

This a survey on a series of recent papers in collaboration with Emanuele Spadaro on the regularity of area-minimizing currents in codimension higher than $1$.