Pisheng Ding
Published 2018-11-10Version 1
For a harmonic function u on Euclidean space, this note shows that |grad(u)| is essentially determined by the geometry of level hypersurfaces of u. 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.
Reverse approximation of gradient flows as Minimizing Movements: a conjecture by De Giorgi
Local behaviour of the gradient flow of an analytic function near the unstable set of a critical point
On volumes determined by subsets of Euclidean space
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