Weyl law for the volume spectrum

Yevgeny Liokumovich; Fernando C. Marques; André Neves

doi:https://doi.org/10.4007/annals.2018.187.3.7

Pages 933-961 from Volume 187 (2018), Issue 3 by Yevgeny Liokumovich, Fernando C. Marques, André Neves

Abstract

Given $M$ a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum $\{\omega _p(M)\}_{p\in \mathbb {N}}$ satisfies a Weyl law that was conjectured by Gromov.

Milestones

Received: 8 December 2017
Revised: 9 February 2018
Accepted: 12 February 2018
Published online: 27 March 2018

Authors

Yevgeny Liokumovich

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA

Fernando C. Marques

Department of Mathematics, Princeton University, Princeton, NJ

André Neves

Department of Mathematics, University of Chicago, Chicago, IL and Imperial College London, London, UK