## Kodai Mathematical Journal

### $L^{p}$ $p$-harmonic 1-forms on locally conformally flat Riemannian manifolds

#### Abstract

In this paper, we obtain some vanishing and finiteness theorems for $L^{p}$ $p$-harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of $M$ is bounded by a suitable constant.

#### Article information

Source
Kodai Math. J., Volume 40, Number 3 (2017), 518-536.

Dates
Revised: 27 December 2016
First available in Project Euclid: 31 October 2017

https://projecteuclid.org/euclid.kmj/1509415230

Digital Object Identifier
doi:10.2996/kmj/1509415230

Mathematical Reviews number (MathSciNet)
MR3718495

Zentralblatt MATH identifier
1384.53038

#### Citation

Han, Yingbo; Zhang, Qianyu; Liang, Mingheng. $L^{p}$ $p$-harmonic 1-forms on locally conformally flat Riemannian manifolds. Kodai Math. J. 40 (2017), no. 3, 518--536. doi:10.2996/kmj/1509415230. https://projecteuclid.org/euclid.kmj/1509415230