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The anisotropic Weyl law and Grassmannian equidistribution
Abstract
We establish a Weyl law for the codimension-one anisotropic volume spectrum on compact Riemannian manifolds. We then use this law to obtain equidistribution in the full Grassmannian bundle while keeping the ambient metric fixed. More precisely, on every closed connected smooth Riemannian manifold of dimension three through six, we construct smooth, embedded hypersurfaces stationary for anisotropies smoothly converging to area. The cumulative sum of their area measures, when lifted to the Grassmannian bundle, converges to the uniform measure.
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BibTeX
@misc{rosa2026anisotropic,
title = {{The anisotropic Weyl law and Grassmannian equidistribution}},
author = {Antonio De Rosa and Aria Halavati},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18599},
eprint = {2610.18599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18599},
}
RIS
TY - UNPB
TI - The anisotropic Weyl law and Grassmannian equidistribution
AU - Antonio De Rosa
AU - Aria Halavati
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18599
UR - https://arxiv.org/abs/2610.18599
AB - We establish a Weyl law for the codimension-one anisotropic volume spectrum on compact Riemannian manifolds. We then use this law to obtain equidistribution in the full Grassmannian bundle while keeping the ambient metric fixed. More precisely, on every closed connected smooth Riemannian manifold of dimension three through six, we construct smooth, embedded hypersurfaces stationary for anisotropies smoothly converging to area. The cumulative sum of their area measures, when lifted to the Grassmannian bundle, converges to the uniform measure.
ER -