An extension of Jörgens–Calabi–Pogorelov theorem to parabolic Monge–Ampère equation

Abstract

We extend a theorem of Jorgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampere equation to parabolic Monge–Ampere equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension $$n\ge 3$$ , the work of Gutierrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampere equations.