Methods and Applications of Analysis
Volume 13 (2006)
The Inverse Mean Curvature Flow in Robertson-Walker Spaces and its Application
Pages: 19 – 28
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