On the Gradient of Harmonic Functions
Classical Analysis and ODEs
2018-12-07 v2 Analysis of PDEs
Differential Geometry
Abstract
For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely determined by the mean curvature of the level hypersurfaces intersecting the flow.
Cite
@article{arxiv.1811.04204,
title = {On the Gradient of Harmonic Functions},
author = {Pisheng Ding},
journal= {arXiv preprint arXiv:1811.04204},
year = {2018}
}