Entire mean curvature flows of graphs

Xiaoli Han

Vol. 236 (2008), No. 2, 333–339

DOI: 10.2140/pjm.2008.236.333

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 2000

Primary: 53C44

Secondary: 53C21

Milestones

Received: 25 June 2007

Revised: 21 January 2008

Accepted: 12 March 2008

Published: 1 June 2008