Vol. 309, No. 1, 2020

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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
Authors
Shoo Seto
Department of Mathematics
California State University, Fullerton
Fullerton, CA
United States