Comparison of the real and the complex Green functions, and sharp estimates of the Kobayashi distance

Nikolai Nikolov (1) , Pascal J. Thomas (2, 3)

1 Institute of Mathematics and Informatics
2 LEP - Laboratoire Émile Picard
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We extend the upper estimates obtained by M. Carlehed and B.-Y. Chen about the ratio of the classical and pluricomplex Green functions to the case of $\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type. We also give some lower estimates. In order to obtain those results, and because it is of independent interest, we refine and unify some classical estimates about the Kobayashi distance and the Lempert function in such domains.

Domaines: Variables complexes [math.CV]

Nikolai Nikolov, Pascal J. Thomas. Comparison of the real and the complex Green functions, and sharp estimates of the Kobayashi distance. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2018, 18 (3), pp.1125--1143. ⟨10.2422/2036-2145.201608_027⟩. ⟨hal-01620894⟩