A Counterexample to a Conjecture by Blocki-Zwonek

作者：Ahag P; Czyz R; Lundow P H^*

来源：Experimental Mathematics, 2018, 27(1): 119-124.

DOI：10.1080/10586458.2016.1230913

• Blocki-Zwonek conjectures
• Bergman kernel
• Green functions
• Jacobi functions

For a bounded pseudoconvex domain Omega subset of C-n and pluricomplex Green function g(Omega) (z, a) with pole at a is an element of Omega, itwas conjectured by Blocki and Zwonek that beta(t) = log lambda(n) ({z is an element of Omega: g(Omega) (z, a) < t}) is a convex function on (-infinity, 0). With Omega the annulus A(2) = {z is an element of C : 1/2 < vertical bar z vertical bar < 2} the Green function g(Omega) (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 beta is not convex.

• 出版日期2018