Volume preserving mean curvature flow in the hyperbolic space

By E. Rivas, Vicente F. Miquel Molina. 2007

61 citations recorded by the source corpus.

. We prove: "If M 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 M is not convex by horospheres but it is close enough to a geodesic sphere.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4e186df54eb995cfa32fc5794971caa0a7af99d7

How researchers see this paper

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In Applied Mathematics

1. Carlo Sinestrari
2. Esther Cabezas-Rivas
3. Qi Ding
4. Robert Haslhofer
5. Ludovic Rifford
6. S. Brendle
7. G. Huisken
8. Bruce Kleiner

In Geometry and Topology

1. Carlo Sinestrari
2. Esther Cabezas-Rivas
3. Qi Ding
4. Robert Haslhofer
5. S. Brendle
6. G. Huisken
7. Bruce Kleiner

Citations in the corpus

• Volume-preserving flow by powers of the mth mean curvature (2009, background): “Recently, the first author and Miquel [ 9 ] considered volume-preserving mean curvature flow in hyperbolic space and proved convergence to geodesic spheres.”
• The inverse mean curvature flow in rotationally symmetric spaces (2011, background): “Evolution equations are very helpful for estimates of asymptotic behavior and long time existence (see [ 1 , 2, 12] for instance).”