Multilinear Kakeya and Michael-Simon inequality for anisotropic stationary varifolds

Abstract: 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.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Virtual Maxwell Analysis Seminar

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