English

Volume preserving mean curvature flow in the Hyperbolic space

Differential Geometry 2007-05-23 v1

Abstract

We prove: "If MM is a compact hypersurface of the hyperbolic space, convex by horospheres and evolving by the volume preserving mean curvature flow, then it flows for all time, convexity by horospheres is preserved and the flow converges, exponentially, to a geodesic sphere". In addition, we show that the same conclusions about long time existence and convergence hold if MM is not convex by horospheres but it is close enough to a geodesic sphere.

Keywords

Cite

@article{arxiv.math/0611216,
  title  = {Volume preserving mean curvature flow in the Hyperbolic space},
  author = {Esther Cabezas-Rivas and Vicente Miquel},
  journal= {arXiv preprint arXiv:math/0611216},
  year   = {2007}
}
R2 v1 2026-07-22T17:45:55.801Z