Geodesic
Estimates for the Bergman kernel and metric of convex domains in ${\Bbb C}^n$
Nikolai Nikolov1 ; Peter Pflug2
1Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
2Fachbereich Mathematik Carl von Ossietzky Universität Oldenburg Postfach 2503 D-26111 Oldenburg, Germany
Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 73-78
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Sharp geometrical lower and upper estimates are obtained for the Bergman kernel on the diagonal of a convex domain $D\subset {{\mathbb C}}^n$ which does not contain complex lines. It is also proved that the ratio of the Bergman and Carathéodory metrics of $D$ does not exceed a constant depending only on $n$.
DOI : 10.4064/ap81-1-6
Keywords: sharp geometrical lower upper estimates obtained bergman kernel diagonal convex domain subset mathbb which does contain complex lines proved ratio bergman carath odory metrics does exceed constant depending only

Nikolai Nikolov  1   ; Peter Pflug  2

1 Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
2 Fachbereich Mathematik Carl von Ossietzky Universität Oldenburg Postfach 2503 D-26111 Oldenburg, Germany 
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 metric of convex domains in ${\Bbb C}^n$},
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 metric of convex domains in ${\Bbb C}^n$
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 metric of convex domains in ${\Bbb C}^n$
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Nikolai Nikolov; Peter Pflug. Estimates for the Bergman kernel and
 metric of convex domains in ${\Bbb C}^n$. Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 73-78. doi: 10.4064/ap81-1-6

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