대한수학회지 (Journal of the Korean Mathematical Society)

  • 제55권4호
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  • Pages.897-921
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  • 2018
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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GEOMETRIC ANALYSIS ON THE DIEDERICH-FORNÆSS INDEX

  • 투고 : 2017.08.02
  • 심사 : 2018.01.30
  • 발행 : 2018.07.01
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⟨ 이전 논문 다음 논문 ⟩

초록

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.

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참고문헌

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