A general existence theorem for free-boundary Monge-Ampere equations with prescribed gradient image, applied to degenerate optimal transport, Monge-Ampere eigenvalues, a hemispherical Minkowski problem, and free-boundary toric Kaehler-Ricci solitons.
Pure Appl
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On a general class of free boundary Monge-Amp\`ere equations
A general existence theorem for free-boundary Monge-Ampere equations with prescribed gradient image, applied to degenerate optimal transport, Monge-Ampere eigenvalues, a hemispherical Minkowski problem, and free-boundary toric Kaehler-Ricci solitons.