(untitled) (Analysis in Theory and Applications, 2022)
We consider the Monge-Ampère equation det (D^2u) = f in R^n, where f is a positive bounded periodic function. We prove that u must be the sum of a quadratic polynomial and a periodic function. For f ≡ 1, this is the classic result by Jörgens, Calabi and Pogorelov. For f ∈ C^α, this was proved by Caffarelli and the first named author.