Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Space

@inproceedings{CabezasRivas2008VolumepreservingMC,
  title={Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Space},
  author={Esther Cabezas-Rivas and V Alegre-de Miquel},
  year={2008}
}
In an ambient space with rotational symmetry around an axis (which include the Hyperbolic and Euclidean spaces), we study the evolution under the volume-preserving mean curvature flow of a revolution hypersurface M generated by a graph over the axis of revolution and with boundary in two totally geodesic hypersurfaces (tgh for short). Requiring that, for each time t ≥ 0, the evolving hypersurface Mt meets such tgh ortogonally, we prove that: a) the flow exists while Mt does not touch the axis… CONTINUE READING