# Constant mean curvature, flux conservation, and symmetry

@article{Edelen2013ConstantMC, title={Constant mean curvature, flux conservation, and symmetry}, author={Nick Edelen and Bruce Solomon}, journal={arXiv: Differential Geometry}, year={2013} }

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

#### 2 Citations

Conservation laws for surfaces of constant mean curvature in 3-dimensional space forms

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The exterior differential system for constant mean curvature (CMC) surfaces in a 3-dimensional space form is an elliptic Monge-Ampere system defined on the unit tangent bundle. We determine the… Expand

Helicoidal flat surfaces in the 3-sphere

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In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental… Expand

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