Characterizing Level-set Families of Harmonic Functions
Analysis of PDEs
2023-08-28 v2 Differential Geometry
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.
Cite
@article{arxiv.1812.02198,
title = {Characterizing Level-set Families of Harmonic Functions},
author = {Pisheng Ding},
journal= {arXiv preprint arXiv:1812.02198},
year = {2023}
}