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arXiv · 2609.34573

Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality

Guido De Philippis·Luca Gennaioli·Alessandro Pigati·Filip Rindler
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Abstract

We prove mass estimates for PDE-constrained measures on sets of $σ$-finite ${\mathcal H}^m$-measure, assuming an appropriate rank condition. As an application, we derive a Michael--Simon inequality for varifolds with bounded anisotropic first variation with respect to an integrand that satisfies the natural atomic condition (AC1).

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Guido De Philippis, Luca Gennaioli, Alessandro Pigati, Filip Rindler. 2026-09-28. Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality. https://arxiv.org/abs/2609.34573

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