Constant mean curvature, flux conservation, and symmetry

  title={Constant mean curvature, flux conservation, and symmetry},
  author={Nick Edelen and Bruce Solomon},
  journal={arXiv: Differential Geometry},
As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing this http URL Theorem 3.5 here, we generalize that law by relaxing the topological restrictions assumed in [KKS] and by allowing a weighted mean curvature functional. We also prove a partial converse (Theorem 4.1) which roughly says that when flux is conserved along a Killing field, a hypersurface splits into two regions: one… Expand
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