The anisotropic Michael-Simon inequality for surfaces in every codimension

Abstract

We prove a Michael-Simon inequality for $2$-varifolds in ${\mathbb{R}}^N$, in arbitrary codimension, for anisotropies sufficiently close to the area functional. Building on the ideas of Almgren and De Philippis-Pigati, we introduce a projection method for anisotropic stress measures yielding geometric inequalities that apply in arbitrary dimension and codimension.

arXiv commentWe refer the reader to the companion paper for the general result in every dimension