Regularity of higher codimension area minimizing integral currents

TL;DR

This paper discusses a new proof of the partial regularity of area minimizing currents in higher codimension, based on Almgren's work, with detailed explanations suitable for educational purposes.

Contribution

It provides an expanded, pedagogical version of Almgren's proof of partial regularity for higher codimension area minimizing currents, clarifying complex steps.

Findings

New proof of partial regularity in higher codimension

Clarification of Almgren's original arguments

Educational exposition of advanced geometric measure theory

Abstract

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).