Wormholes, geometric flows and singularities.

In this paper we study the evolution of wormhole geometries under intrinsic geometric flows. We make evolve numerically the time symmetric foliations of a family of spherically symmetric asymptotically flat wormholes under the Ricci flow and under the RG-2 flow. We use some theorems adapted from the compact case for studying the evolution of different wormhole types, specially those with high curvature zones. Some metrics expand and others contract at the beginning of the flow, however, all metrics pinch-off at certain time. We present a numerical study of the evolution of wormhole singularities in three dimensions extending the theoretical estimations. Finally, we calculate numerically the Hamilton's entropy of the surface and show that it is monotonous through the evolution.