Methods and Applications of Analysis

Volume 13 (2006)

Number 1

The Inverse Mean Curvature Flow in Robertson-Walker Spaces and its Application

Pages: 19 – 28



Claus Gerhardt


We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing that in general the transition flow is only of class $C^3$.


Lorentzian manifold, transition from big crunch to big bang, cyclic universe, general relativity, inverse mean curvature flow, ARW spacetimes

2010 Mathematics Subject Classification

35J60, 53C21, 53C44, 53C50, 58J05

Published 1 January 2006