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The anisotropic Michael-Simon inequality for surfaces in every codimension
Abstract
We prove a Michael-Simon inequality for $2$-varifolds in ℝN, 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.
Related
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BibTeX
@misc{firester2026anisotropic,
title = {{The anisotropic Michael-Simon inequality for surfaces in every codimension}},
author = {Benjy Firester and Raphael Tsiamis},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31168},
eprint = {2608.31168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31168},
}
RIS
TY - UNPB
TI - The anisotropic Michael-Simon inequality for surfaces in every codimension
AU - Benjy Firester
AU - Raphael Tsiamis
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31168
UR - https://arxiv.org/abs/2608.31168
AB - We prove a Michael-Simon inequality for $2$-varifolds in 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.
ER -