Calculus of Variations and Geometric Measure Theory

Variational methods and applications

Multilinear Kakeya and Michael-Simon inequality for anisotropic stationary varifolds - (online)

Guido De Philippis (Courant Institute of Mathematics)

created by paolini on 08 Sep 2021
modified on 14 May 2022

6 sep 2021 -- 17:00   [open in google calendar]


Michael Simon inequality ( is a fundamental tool in geometric analysis and geometric measure theory. Its extension to anisotropic integrands will allow to extend to anisotropic integrands a series of results which are currently known only for the area functional.

In this talk I will present an anistropic version of the Michael-Simon inequality, for for two-dimensional varifolds in R3, provided that the integrand is close to the area in the C1-topology. The proof is deeply inspired by posthumous notes by Almgren, devoted to the same result. Although our arguments overlap with Almgren’s, some parts are greatly simplified and rely on a nonlinear version of the planar multilinear Kakaeya inequality.