The distance between minimal hypersurfaces is a viscosity supersolution to an elliptic PDE, with extensions to parabolic PDEs when evolving by mean curvature flow.
Brendle, Two-point functions and their applications in geometry , Bull
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Distance between minimal surfaces and flows
The distance between minimal hypersurfaces is a viscosity supersolution to an elliptic PDE, with extensions to parabolic PDEs when evolving by mean curvature flow.