A free boundary Monge-Amp\`ere equation and applications to complete
Calabi-Yau metrics
A free boundary Monge-Amp\`ere equation and applications to complete
Calabi-Yau metrics
Let $P$ be a convex body containing the origin in its interior. We study a real Monge-Amp\`ere equation with singularities along $\del P$ which is Legendre dual to a certain free boundary Monge-Amp\`ere equation. This is motivated by the existence problem for complete Calabi-Yau metrics on log Calabi-Yau pairs $(X, …