Calculus of Variations and Geometric Measure Theory

C. De Lellis

Almgren's center manifold in a simple setting

created by delellis on 17 Jul 2018
modified on 27 Jun 2019


Lecture Notes

Inserted: 17 jul 2018
Last Updated: 27 jun 2019

Year: 2018

ArXiv: 1807.06239 PDF

Lectures held at Park City 9-13 July 2018


We aim at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi's celebrated $\varepsilon$-regularity theorem and Almgren's center manifold. Both theorems will be proved in a very simplified situation, which however allows to illustrate some of the most important PDE estimates.