Kodai Mathematical Journal

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

Yingbo Han, Qianyu Zhang, and Mingheng Liang

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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

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

Received: 20 September 2016
Revised: 27 December 2016
First available in Project Euclid: 31 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

$p$-harmonic 1-form locally conformally flat


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

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