Coman conjecture for the bidisc

Lukasz Kosinski , Pascal J. Thomas (1, 2) , Wlodzimierz Zwonek (3)

1 LEP - Laboratoire Émile Picard
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 Instytut Matematyki

In the paper we show the equality between the Lempert function and the Green function with two poles with equal weights in the bidisc thus giving the positive answer to a conjecture of Coman in the simplest unknown case. Actually, a slightly more general equality is proven which in some sense is natural when studied from the point of view of the Nevanlinna-Pick problem in the bidisc.

Domaines: Variables complexes [math.CV]

Lukasz Kosinski, Pascal J. Thomas, Wlodzimierz Zwonek. Coman conjecture for the bidisc. Pacific Journal of Mathematics, 2017, 287, pp.411-422. ⟨10.2140/pjm.2017.287.411⟩. ⟨hal-01620899⟩