## Journal of Differential Geometry

### Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry

Christopher Nerz

#### 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.

#### Article information

Source
J. Differential Geom., Volume 109, Number 2 (2018), 257-289.

Dates
First available in Project Euclid: 23 May 2018

https://projecteuclid.org/euclid.jdg/1527040873

Digital Object Identifier
doi:10.4310/jdg/1527040873

Mathematical Reviews number (MathSciNet)
MR3807320

Zentralblatt MATH identifier
1331.53042

#### Citation

Nerz, Christopher. Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry. J. Differential Geom. 109 (2018), no. 2, 257--289. doi:10.4310/jdg/1527040873. https://projecteuclid.org/euclid.jdg/1527040873