ABSTRACT
For a bounded pseudoconvex domain and pluricomplex Green function gΩ(z, a) with pole at a ∈ Ω, it was conjectured by Błocki and Zwonek that β(t) = log λn({z ∈ Ω: gΩ(z, a) < t}) is a convex function on ( − ∞, 0). With Ω the annulus
the Green function gΩ(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.
Acknowledgments
This work was inspired by Ian Kilmister and his Motörhead.