A free boundary Monge-Ampère equation and applications to complete Calabi-Yau metrics

Tristan C. Collins, Freid Tong, Shing-Tung Yau

Let $P$ be a convex body containing the origin in its interior. We study a real Monge-Ampère equation with singularities along $\del P$ which is Legendre dual to a certain free bou…