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

• Nikolai Nikolov ^[1] ; Pascal J. Thomas ^[2]
  1. [1] Faculty of Information Sciences State University of Library Studies and Information Technologies, Bulgaria
  2. [2] Universitè de Toulouse, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 3, 2018, págs. 1125-1143
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We extend the upper estimates obtained by M. Carlehed [2] and B.-Y. Chen [3] about the ratio of the classical and pluricomplex Green functions to the case of C2-smooth locally C-convexifiable domains of finite type. We also give some lower estimates. In order to obtain these 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.