Upper bound for the Lempert function of smooth domains

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

1 Institute of Mathematics and Informatics
2 Institut f¨ur Mathematik,
3 IMT - Institut de Mathématiques de Toulouse UMR5219

An upper estimate for the Lempert function of any $C^{1+\varepsilon}$-smooth bounded domain in $\Bbb C^n$ is found in terms of the boundary distance.

Domaines: Variables complexes [math.CV]

Nikolai Nikolov, Peter Pflug, Pascal J. Thomas. Upper bound for the Lempert function of smooth domains. Mathematische Zeitschrift, 2010, 266 (2), pp.425-430. ⟨10.1007/s00209-009-0577-9⟩. ⟨hal-00334036⟩