Lisa Hed
Approximation of plurisubharmonic functions
We shall consider different kinds of approximation of plurisubharmonic functions on a hyperconvex domain $\Omega$. Especially, we shall look at approximation by plurisubharmonic functions defined on strictly larger domains $\Omega_j$, $\Omega\subset\subset\Omega_j$. In a joint work with U. Cegrell we proved that if we can approximate one function from a certain class of plurisubharmonic functions from outside, then we can approximate all such functions. We shall discuss what geometric conditions $\Omega$ should have for this approximation to work. Finally, we will consider the connection between this approximation and the notion of plurisubharmonic functions defined on compact sets that was introduced by Poletsky.