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arXiv · 1210.1005

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

Romain Gicquaud·Dandan Ji·Yuguang Shi
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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 $1<p<\frac{n-1}{2}$, then $(X^n, g)$ must be asymptotically locally hyperbolic. One interesting application of this theorem is to show a rigidity result for the hyperbolic space under an integral condition for the curvature.

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Romain Gicquaud, Dandan Ji, Yuguang Shi. 2012-10-03. On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvature. https://arxiv.org/abs/1210.1005

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