Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
type: Item
instance of: scholarly article
title: Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
zbMATH Open document ID: 0858.53071
author: Gerhard Huisken
author: Shing-Tung Yau
published in: Inventiones Mathematicae
publication date: 1997-03-10T00:00:00Z
full work available at URL: 00-001M-0000-0013-5B63-3
review text: Let \(N\) be a three-dimensional Riemannian manifold with one end diffeomorphic to \(\mathbb{R}^3\setminus B_1(0)\) such that the metric on \(N\) asymptotically approaches the Euclidean metric near infinity: \(g_{ij} = (1 + 2m/r) \delta_{ij} + O(-r^2)\). By constructing a unique constant mean curvature foliation in the exterior region, there is defined a geometric center of mass at infinity for asymptotically flat ends provided that the mass \(m\) of \(g\), measuring the deviation of \(g\) from the flat metric at infinity, satisfies \(m > 0\). The foliation is interpreted as a geometric center of mass for an infinitely far observer.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C30
zbMATH DE Number: 866093
zbMATH Keywords: constant mean curvature foliation
zbMATH Keywords: center of mass at infinity
zbMATH Keywords: asymptotically flat ends
reviewed by: Petre Stavre
MaRDI profile type: Publication
OpenAlex ID: W2162316402
DOI: 10.1007/S002220050054
description: scientific article; zbMATH DE number 866093