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RISS 인기검색어
- 검색키워드
- 저자 : Krantz, Steven George (검색결과 15 건)
- 무료
- 기관 내 무료
- 유료
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A GEOMETRIC APPROACH TO THE STUDY OF AUTOMORPHISM GROUPS
Krantz, Steven G. Korean Mathematical Society 2016 대한수학회보 Vol.53 No.4
In this paper we study questions about automorphism groups of domains in ${\mathbb{C}}^n$, formulating the ideas entirely in terms of metric geometry. We also provide some applications.
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THE LIMITING CASE OF SEMICONTINUITY OF AUTOMORPHISM GROUPS
KRANTZ, STEVEN G. Korean Mathematical Society 2015 대한수학회보 Vol.52 No.4
In this paper we study the semicontinuity of the automorphism groups of domains in multi-dimensional complex space. We give examples to show that known results are sharp (in terms of the required boundary smoothness).
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APPROXIMATION BY HOLOMORPHIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES
Krantz, Steven G.,Min, Baili Korean Mathematical Society 2020 대한수학회지 Vol.57 No.5
Inspired by a classical approximation result of Bagemihl and Seidel on the disc, we provide generalized results on some proper domains in ℂ<sup>n</sup> about approximation of a continuous function by a holomorphic function in the Mergelyan's style.
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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.
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FATOU THEOREMS OLD AND NEW: AN OVERVIEW OF THE BOUNDARY BEHAVIOR OF HOLOMORPHIC FUNCTIONS
Krantz, Steven G. Korean Mathematical Society 2000 대한수학회지 Vol.37 No.2
We consider the boundary behavior of a Hardy class holomorphic function, either on the disk D in the complex plane or on a domain in multi-dimensional complex space. Although the two theories are formally different, we postulate some unifying fearures, and we suggest some future directions for research.
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THE LIMITING CASE OF SEMICONTINUITY OF AUTOMORPHISM GROUPS
Steven G. Krantz 대한수학회 2015 대한수학회보 Vol.52 No.4
In this paper we study the semicontinuity of the automorphism groups of domains in multi-dimensional complex space. We give examples to show that known results are sharp (in terms of the required boundary smoothness).
-
A geometric approach to the study of automorphism groups
Steven G. Krantz 대한수학회 2016 대한수학회보 Vol.53 No.4
In this paper we study questions about automorphism groups of domains in $\mathbb C^n$, formulating the ideas entirely in terms of metric geometry. We also provide some applications.
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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.
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CHARACTERIZATION OF REINHARDT DOMAINS BY THEIR AUTOMORPHISM GROUPS
Isaen, Alexander-V.,Krantz, Steven-G. Korean Mathematical Society 2000 대한수학회지 Vol.37 No.2
We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.
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