# Solutions to the Monge-Ampere equation with polyhedral and Y-shaped singularities

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The Monge-Ampere equation det(D^2 u) = 1 arises in prescribed

curvature problems and in optimal transport. An interesting feature of the

equation is that it admits singular solutions. We will discuss new examples

of convex functions on R^n that solve the Monge-Ampere equation away from

finitely many points, but contain polyhedral and Y-shaped singular

structures. Along the way we will discuss geometric and applied motivations

for constructing such examples, as well as their connection to a certain

obstacle problem.