A Liouville Theorem for the Complex Monge-Ampère Equation

Abstract

In this note, we derive a Liouville theorem for the complex Monge-Ampère equation. Our result states that if the global solution $u$ of the complex Monge-Ampère equation with constant right-hand side differs from a quadratic polynomial solution by $o(\abs{x}^2)$ at infinity, then $u$ is a quadratic polynomial.

References in corpus (1)

• A Viscosity Approach to the Dirichlet Problem for Complex Monge-Ampère Equations

Cited by in corpus (1)

• A Liouville Theorem on the PDE $\det (f_{i\bar{j}})=1$