# On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvature

Abstract : In this paper we consider the geometric behavior near infinity of some Einstein manifolds $(X^n, g)$ with Weyl curvature belonging to a certain $L^p$ space. Namely, we show that if $(X^n, g)$, $n \geq 7$, admits an essential set and has its Weyl curvature in $L^p$ for some \$1
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https://hal.archives-ouvertes.fr/hal-00783613
Contributor : Romain Gicquaud <>
Submitted on : Friday, February 1, 2013 - 1:22:28 PM
Last modification on : Thursday, March 5, 2020 - 5:33:22 PM

### Identifiers

• HAL Id : hal-00783613, version 1
• ARXIV : 1210.1005

### Citation

Romain Gicquaud, Dandan Ji, Yuguang Shi. On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvature. Communications in Analysis and Geometry, International Press, 2013, 21 (5), pp.1081-1113. ⟨hal-00783613⟩

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