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

@misc{philippis2026scaleinvariant,
  title = {{Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality}},
  author = {Guido De Philippis and Luca Gennaioli and Alessandro Pigati and Filip Rindler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34573},
  eprint = {2609.34573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34573},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
AU  - Guido De Philippis
AU  - Luca Gennaioli
AU  - Alessandro Pigati
AU  - Filip Rindler
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34573
UR  - https://arxiv.org/abs/2609.34573
AB  - We prove mass estimates for PDE-constrained measures on sets of σ-finite 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).
ER  -