Parametric inequalities and Weyl law for the volume spectrum

Autor:	Guth, Larry, Liokumovich, Yevgeny
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Geometric Topology Mathematics - Spectral Theory 35P20 53A10
Druh dokumentu:	Working Paper
Popis:	We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities: isoperimetric inequality and coarea inequality. We prove two such generalizations in low dimensions and obtain the Weyl law for 1-cycles in 3-manifolds. We also give a new proof of the Almgren isomorphism theorem. Comment: To appear in Geom. Top
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.11805 Zobrazit plný text záznamu View this record from Arxiv