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 objects that in turn yield the preservation of certain quantities, such as the positivity of the fractional mean curvature.
|Number of pages||39|
|Journal||Communications in Analysis and Geometry|
|Publication status||Published - 2019|