Current Developments in Mathematics

Volume 2014

The regularity of minimal surfaces in higher codimension

Pages: 153 – 229



Camillo De Lellis (Mathematik Institut, Universität Zürich, Switzerland)


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

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