Abstract

We consider the evolution of the graph of f : Rⁿ → Rⁿ in Rⁿ × Rⁿ by the mean curvature flow. We prove that the flow exists smoothly for all time if the differential of f has a positive lower bound. Moreover, at each time, the flow remains the graph of a map f_t.

Keywords

graph, Jacobian of the projection

Mathematical Subject Classification

Primary: 53C44

Secondary: 53C21

Authors