A note on inverse curvature flows in ARW spacetimes

TL;DR

This paper proves that in ARW spacetimes, the rescaled inverse curvature flow's leaves converge to a flat graph, providing insights into the geometric behavior of such flows.

Contribution

It establishes the convergence of rescaled inverse curvature flow leaves to a constant graph in ARW spacetimes, extending previous results in geometric flow theory.

Findings

Rescaled curvature flow leaves converge to a constant graph.

The convergence result applies specifically to ARW spacetimes.

Provides a geometric understanding of inverse curvature flows in this setting.

Abstract

We prove that the leaves of the rescaled curvature flow considered in arXiv:math/0403485 [math.DG] converge to the graph of a constant function.