Current Developments in Mathematics
The regularity of minimal surfaces in higher codimension
Pages: 153 – 229
In this paper we review the regularity theory for area minimizing $m$-dimensional currents in codimension higher than $1$, which bounds the dimension of the singular set with $m-2$. In recent joint works with Emanuele Spadaro we have revisited the pioneering program of Almgren, bringing some new techniques from metric analysis and some new ideas to deal with the most intricate aspects of the proof.
integer rectifiable currents, regularity, area minimizing, multiple valued functions
2010 Mathematics Subject Classification
49N60, 49Q05, 49Q15