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arXiv · 1812.02198

Characterizing Level-set Families of Harmonic Functions

Pisheng Ding
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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.

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Pisheng Ding. 2018-12-05. Characterizing Level-set Families of Harmonic Functions. https://doi.org/10.1007/s41478-019-00218-9

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