English

Weyl law for 1-cycles

Differential Geometry 2025-11-18 v2 Metric Geometry

Abstract

We prove the Weyl law for the volume spectrum for 11-cycles in nn-dimensional manifolds which was conjectured by Gromov. We follow the strategy of Guth and Liokumovich of obtaining the Weyl law from parametric versions of the coarea inequality and the isoperimetric inequality. A version of the later for families of 00-cycles is shown in this article. We also obtain approximation results by δ\delta-localized families, which are used to prove the parametric inequalities.

Keywords

Cite

@article{arxiv.2410.23192,
  title  = {Weyl law for 1-cycles},
  author = {Bruno Staffa},
  journal= {arXiv preprint arXiv:2410.23192},
  year   = {2025}
}

Comments

Improved exposition. Submitted

R2 v1 2026-06-28T19:41:39.598Z