The first nonzero eigenvalue of the $p$-Laplacian on differential forms

Shoo Seto

Vol. 309 (2020), No. 1, 213–222

DOI: 10.2140/pjm.2020.309.213

Abstract

We introduce a generalization of the $p$-Laplace operator to act on differential forms and generalize an estimate of Gallot and Meyer (1973) for the first nonzero eigenvalue on closed Riemannian manifolds.

Keywords

differential forms, Hodge Laplacian, $p$-Laplacian, Weitzenböck curvature

Mathematical Subject Classification 2010

Primary: 47J10, 53C65

Milestones

Received: 2 April 2019

Revised: 19 December 2019

Accepted: 29 June 2020

Published: 26 December 2020