Inverse mean curvature flows in the hyperbolic 3-space revisited

TL;DR

This paper revisits inverse mean curvature flows in hyperbolic 3-space, demonstrating that the limiting shape may not be round after scaling, which clarifies previous inconsistencies in the literature.

Contribution

It provides a revised understanding of the asymptotic shape of inverse mean curvature flows in hyperbolic space, correcting prior assumptions.

Findings

Limiting shape is not necessarily round after scaling

Resolves an inconsistency in previous literature

Provides new insights into geometric flow behavior in hyperbolic space

Abstract

This note revisits the inverse mean curvature flow in the 3-dimensional hyperbolic space. In particular, we show that the limiting shape is not necessarily round after scaling, thus resolving an inconsistency in the literature.