Weak solutions to the complex Hessian equation
We investigate the class of functions associated with the complex Hessian equation .
Weak solutions to the complex Monge-Ampère equation on hyperconvex domains
We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.
Weighted pluripotential theory on compact Kähler manifolds
We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions