Inserted: 12 nov 2015
Last Updated: 24 may 2017
Journal: Boll. Unione Mat. Ital.
To appear in Bollettino UMI
This note is a survey on the optimal regularity theory for $2$-dimensional area minimizing surfaces and some perturbative cases in codimension higher than $1$. The survey is based on four recent joint papers with Emanuele Spadaro and Luca Spolaor.