An optimal transport approach to Monge-Amp\`ere equations on compact Hessian manifolds

11 Jul 2016 Hultgren Jakob Önnheim Magnus

In this paper we consider Monge-Amp\`ere equations on compact Hessian manifolds, or equivalently Monge-Amp\`ere equations on certain unbounded convex domains $\Omega\subseteq \mathbb{R}^n$, with a periodicity constraint given by the action of an affine group. In the case where the affine group action is volume-preserving, i.e., when the manifold is special, the solvability of the corresponding Monge-Amp\`ere equation was established using the continuity method by Cheng and Yau... (read more)

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  • DIFFERENTIAL GEOMETRY
  • COMPLEX VARIABLES