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http://dx.doi.org/10.4134/JKMS.j170515

GEOMETRIC ANALYSIS ON THE DIEDERICH-FORNÆSS INDEX  

Krantz, Steven George (Mathematics Department Washington University)
Liu, Bingyuan (Mathematics Department University of California)
Peloso, Marco Maria (Dipartimento di Matematica Universita degli Studi di Milano)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.4, 2018 , pp. 897-921 More about this Journal
Abstract
Given bounded pseudoconvex domains in 2-dimensional complex Euclidean space, we derive analytical and geometric conditions which guarantee the Diederich-$Forn{\ae}ss$ index is 1. The analytical condition is independent of strongly pseudoconvex points and extends $Forn{\ae}ss$-Herbig's theorem in 2007. The geometric condition reveals the index reflects topological properties of boundary. The proof uses an idea including differential equations and geometric analysis to find the optimal defining function. We also give a precise domain of which the Diederich-$Forn{\ae}ss$ index is 1. The index of this domain can not be verified by formerly known theorems.
Keywords
Diederich-$Forn{\ae}ss$ index; pseudoconvex; domain; plurisubharmonic;
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