On the Maximal Rank Problem for the Complex Homogeneous Monge-Ampère Equation

Abstract

We give examples of regular boundary data for the Dirichlet problem for the Complex Homogeneous Monge-Ampère Equation over the unit disc, whose solution is completely degenerate on a non-empty open set and thus fails to have maximal rank.

10 pages

References in corpus (1)

• Applications of the duality between the Complex Monge-Ampère Equation and the Hele-Shaw flow

Cited by in corpus (3)

• On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics
• A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials
• Geodesic Convexity of Small Neighborhood in the Space of Kähler Potentials