On the Gradient of Harmonic Functions
classification
🧮 math.CA
math.APmath.DG
keywords
gradientdeterminedflowharmonichypersurfaceslevelalongchanges
read the original 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.