arXiv subjects
Publications and source records attributed to Håkan Persson.
Let $M$ be an $n$-dimensional complex manifold. A holomorphic function $f:M\to \mathbb C$ is said to be semi-Bloch if for every $λ\in \mathbb C$ the function $g_λ=\exp(λf(z))$ is normal on $M$. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.
We study the problem of approximating plurisubharmonic functions on a bounded domain $Ω$ by continuous plurisubharmonic functions defined on neighborhoods of $\barΩ$. It turns out that this problem can be linked to the problem of solving a Dirichlet type problem for functions plurisubharmonic on the compact set $\barΩ$ in the sense of Poletsky. A stronger notion of hyperconvexity is introduced to fully utilize this connection, and we show that for this class of domains the duality between the two problems is perfect. In this setting, we give a characterization of plurisubharmonic boundary values, and prove some theorems regarding the approximation of plurisubharmonic functions.
Using techniques from the analysis of PDEs to study the boundary behaviour of functions on domains with low boundary regularity, we extend results by Fornaæss-Wiegerinck (1989) on plurisubharmonic approximation and by Demailly (1987) on the existence on bounded plurisubharmonic exhaustion functions to domains beyond Lipschitz boundary regularity.