An integral inequality of an intrinsic measure on bounded domains in \({\mathbb{C}{}}^ n\)
Let \(K_ D\) denote the Eisenman-Kobayashi volume element (defined using the unit ball) on a strongly pseudoconvex domain \(D\) in \(\mathbb{C}^ n\). \textit{I. Graham} and \textit{H. Wu} [Trans. Am. Math. Soc. 288, No. 2, 625- 660 (1985; Zbl 0582.32034)] have shown that \(K_ D\) need not be logarithmically plurisubharmonic. The authors prove that \(K_ D\) satisfies an integral inequality, weaker than logarithmic plurisubharmonicity, on analytically embedded disks sufficiently close to the boundary of \(D\). Moreover, a similar inequality holds for any bounded domain on which the Eisenman-Kobayashi volume element satisfies a suitable boundary growth condition.
scientific article; zbMATH DE number 168030
scientific article