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Conformal compactification of asymptotically locally hyperbolic metrics II: Weakly ALH metrics

Abstract : In this paper we pursue the work initiated in \cite{Bahuaud, BahuaudGicquaud}: study the extent to which conformally compact asymptotically hyperbolic metrics can be characterized intrinsically. We show how the decay rate of the sectional curvature to -1 controls the Hölder regularity of the compactified metric. To this end, we construct harmonic coordinates that satisfy some Neumann-type condition at infinity. Combined with a new integration argument, this permits us to recover to a large extent our previous result without any decay assumption on the covariant derivatives of the Riemann tensor. We believe that our result is optimal.
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https://hal.archives-ouvertes.fr/hal-00783625
Contributor : Romain Gicquaud <>
Submitted on : Friday, February 1, 2013 - 1:31:52 PM
Last modification on : Thursday, March 5, 2020 - 5:33:44 PM

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  • HAL Id : hal-00783625, version 1
  • ARXIV : 1109.5096

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Romain Gicquaud. Conformal compactification of asymptotically locally hyperbolic metrics II: Weakly ALH metrics. Communications in Partial Differential Equations, Taylor & Francis, 2013, 38 (8), pp.1313-1367. ⟨hal-00783625⟩

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