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arXiv · 1811.04204

On the Gradient of Harmonic Functions

Pisheng Ding
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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.

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Pisheng Ding. 2018-11-10. On the Gradient of Harmonic Functions. https://arxiv.org/abs/1811.04204

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