Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry
type: Item
instance of: scholarly article
title: Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry
zbMATH Open document ID: 1420.53031
author: Christopher Nerz
published in: Journal of Differential Geometry
publication date: 2018-05-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1501.02197
full work available at URL: https://projecteuclid.org/euclid.jdg/1527040873
review text: The author deals with foliations by spheres of constant expansion near infinity (CE), useful in general relativity. In [Invent. Math. 124, No. 1--3, 281--311 (1996; Zbl 0858.53071)], \textit{G. Huisken} and \textit{S.-T. Yau} proved that, near infinity, every Riemannian manifold is uniquely foliated by stable surfaces with constant mean curvature (CMC) if it is asymptotically equal to the Schwarzschild solution and has positive mass. Their decay assumptions were subsequently weakened by \textit{J. Metzger} [J. Differ. Geom. 77, No. 2, 201--236 (2007; Zbl 1140.53013)] and other authors. The paper under review extends the setting to asymptotically flat initial data sets with non-vanishing ADM mass, assumes weaker decay conditions on the metric \(g\), and partly replaces the decay condition of $k$ by an integral smallness condition. In addition, it is shown that the unique CE-surfaces constructed are asymptotically independent of time if the linear momentum vanishes. This result is motivated by earlier work of the author on the time evolution of CMC spheres.
reviewed by: Antonio De Nicola
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 6877020
zbMATH Keywords: foliation
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
OpenAlex ID: W2962742291
Wikidata QID: Q115165684
arXiv ID: 1501.02197
DOI: 10.4310/JDG/1527040873
description: scientific article