arXiv subjects
Publications and source records attributed to Benedikt Steinar Magnusson.
We give a characterization of stratified totally real sets that admit Carleman approximation by entire functions. As an application we show that the product of two stratified totally real Carleman continua is a Carleman continuum.
Using a recent result of Lárusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in complex projective space. As a corollary we get a characterization of the projective hull for connected compact sets in complex projective space by the existence of analytic discs.
We generalize the Poletsky disc envelope formula for the function $\sup \{u \in \PSH(X,ω) ; u\leq ϕ\}$ on any complex manifold $X$ to the case where the real (1,1)-current $ω=ω_1-ω_2$ is the difference of two positive closed (1,1)-currents and $ϕ$ is the difference of an $ω_1$-upper semicontinuous function and a plurisubharmonic function.
For each closed, positive (1,1)-current ωon a complex manifold X and each ω-upper semicontinuous function ϕon X we associate a disc functional and prove that its envelope is equal to the supremum of all ω-plurisubharmonic functions dominated by ϕ. This is done by reducing to the case where ωhas a global potential. Then the result follows from Poletsky's theorem, which is the special case ω=0. Applications of this result include a formula for the relative extremal function of an open set in X and, in some cases, a description of the ω-polynomial hull of a set.
We prove a disc formula for the weighted Siciak-Zahariuta extremal function $V_{X,q}$ for an upper semicontinuous function $q$ on an open connected subset $X$ in $\C^n$. This function is also known as the weighted Green function with logaritmic pole at infinity and weighted global extremal function.