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GEOMETRIC ANALYSIS ON THE DIEDERICH-FORNÆSS INDEX
Krantz, Steven George,Liu, Bingyuan,Peloso, Marco Maria Korean Mathematical Society 2018 대한수학회지 Vol.55 No.4
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.
Geometric analysis on the Diederich--Forn\ae ss index
Steven George Krantz,Bingyuan Liu,Marco Maria Peloso 대한수학회 2018 대한수학회지 Vol.55 No.4
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.