The regularity theory for the area functional (in geometric measure theory)
Camillo De Lellis
School of Mathematics, Institute for Advanded Study, 1 Einstein Drive, Princeton, NJ 08540, USA
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Abstract
The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments, and of some of the remaining challenges.