A Counterexample to a Conjecture by Błocki–Zwonek. Issue 1 (2nd January 2018) - Åhag, P.; Czyż, R.; Lundow, P. H.
ABSTRACT: For a bounded pseudoconvex domain and pluricomplex Green function g Ω ( z, a ) with pole at a ∈ Ω, it was conjectured by Błocki and Zwonek that β( t ) = log λ n ( z ∈ Ω: g Ω ( z, a ) < t ) is a convex function on ( − ∞, 0). With Ω the annulus the Green function g Ω ( z, a ) with pole at a = 1 + 0i can be explicitly given in terms of Jacobi theta functions. We show numerically that in this case β is not convex.