Bedford–Taylor theory

Summary

Bedford–Taylor theory defines the complex Monge–Ampère operator $(dd^c u)^n$ for plurisubharmonic functions $u$ that are only locally bounded, not differentiable. The products $dd^c u_1 \wedge \cdots \wedge dd^c u_k$ are defined inductively as closed positive currents, and they are continuous along decreasing sequences of plurisubharmonic functions. Eric Bedford and B. A. Taylor developed the theory in work published in 1976 and 1982. It gives the Monge–Ampère capacity and solves the Dirichlet problem for the complex Monge–Ampère equation with continuous data on strongly pseudoconvex domains. It is the starting point of modern pluripotential theory.