On the evolution by fractional mean curvature
- Sáez, Mariel
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 35K93 53A10
- nonlocal mean curvature, geometric motions, evolving surfaces
In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions.