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

## TL;DR

This paper extends the $p$-Laplacian to differential forms and generalizes an eigenvalue estimate for closed Riemannian manifolds, broadening the understanding of spectral properties in geometric analysis.

## Contribution

It introduces a new $p$-Laplacian operator on differential forms and generalizes Gallot-Meyer's eigenvalue estimate for the first nonzero eigenvalue.

## Key findings

- Generalization of the $p$-Laplacian to differential forms
- Extended eigenvalue estimate for closed Riemannian manifolds
- Potential applications in geometric analysis and spectral theory

## Abstract

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