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June 2018 Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry
Christopher Nerz
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J. Differential Geom. 109(2): 257-289 (June 2018). DOI: 10.4310/jdg/1527040873

Abstract

Motivated by the foliation by stable spheres with constant mean curvature constructed by Huisken–Yau, Metzger proved that every initial data set can be foliated by spheres with constant expansion (CE) if the manifold is asymptotically equal to the standard $[t=0]$-timeslice of the Schwarzschild solution. In this paper, we generalize his result to asymptotically flat initial data sets and weaken additional smallness assumptions made by Metzger. Furthermore, we prove that the CE-surfaces are in a well-defined sense (asymptotically) independent of time if the linear momentum vanishes.

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Christopher Nerz. "Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry." J. Differential Geom. 109 (2) 257 - 289, June 2018. https://doi.org/10.4310/jdg/1527040873

Information

Received: 18 May 2015; Published: June 2018
First available in Project Euclid: 23 May 2018

zbMATH: 1331.53042
MathSciNet: MR3807320
Digital Object Identifier: 10.4310/jdg/1527040873

Rights: Copyright © 2018 Lehigh University

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Vol.109 • No. 2 • June 2018
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