51. The family of level sets of a harmonic function
- Author
-
Pisheng Ding
- Subjects
Algebra and Number Theory ,Mean curvature ,Applied Mathematics ,Mathematical analysis ,symbols.namesake ,Harmonic function ,Flow (mathematics) ,Special functions ,Fourier analysis ,symbols ,Geometry and Topology ,Balanced flow ,Analysis ,Mathematics ,Geometric data analysis - 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.
- Published
- 2019