Characterizing Level-set Families of Harmonic Functions
arXiv:1812.02198 · doi:10.1007/s41478-019-00218-9
Abstract
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from geometric data. As a by-product, it is shown that the evolution of the gradient of a harmonic function along the gradient flow is determined by the mean curvature of the level sets that the flow intersects.