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A geometric approach to the study of automorphism groups

Steven G. Krantz
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회보 (Bulletin of the KMS)|제53권 제4호|pp. 1043-1049

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참고문헌

키워드

automorphism groupboundary orbit accumulation pointinvariant metricKobayashi metric
주제분류수학

초록

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.

Abstract

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.

참고문헌 (16)

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  3. R. E. Greene, "The Geometry of Complex Domains" (2011), Birkhauser
  4. R. E. Greene, "The automorphism groups of strongly pseudoconvex domains", Math. Ann, 261(4), pp.425~446 (1982)
  5. R. E. Greene, "Deformations of complex structure, estimates for the ∂-equation, and stability of the Bergman kernel", Adv. in Math, 43(1), pp.1~86 (1982)
  6. R. E. Greene, "Characterizations of certain weakly pseudo-convex domains with non-compact automorphism groups", Complex Analysis Seminar, pp.121~157 (1987)
  7. K.-T. Kim, "A Kobayashi metric version of Bun Wong’s theorem", Complex Var. Elliptic Equ, 54(3-4), pp.355~369 (2009)
  8. S. Kobayashi, "Hyperbolic Manifolds and Holomorphic Mappings" (1970), Dekker
  9. S. Kobayashi, "On automorphisms of a Kahlerian structure", Nagoya Math. J, 11, pp.115~124 (1957)
  10. S. G. Krantz, "Function Theory of Several Complex Variables" (2001), American Mathematical Society
  11. S. G. Krantz, "Convergence of automorphisms and semicontinuity of automorphism groups", Real Anal. Exchange, 36(2), pp.421~433 (2010)
  12. L. Lempert, "La metrique Kobayashi et las representation des domains sur la boule", Bull. Soc. Math. France, 109(4), pp.427~474 (1981)
  13. J.-P. Rosay, "Sur une characterization de la boule parmi les domains de Cn par son groupe d’automorphismes", Ann. Inst. Fourier (Grenoble), 29(4), pp.91~97 (1979)
  14. H. Seshadri, "On isometries of the Carath´eodory and Kobayashi metrics on strongly pseudoconvex domains", Ann. Sc. Norm. Super. Pisa Cl. Sci, 5(3), pp.393~417 (2006)
  15. K. Verma, "Lecture at BIRS", ~ (2006)
  16. B. Wong, "Characterizations of the unit ball in Cn by its automorphism group", Invent. Math, 41(3), pp.253~257 (1977)

관련 논문AI추천

THE LIMITING CASE OF SEMICONTINUITY OF AUTOMORPHISM GROUPSSteven G. Krantz대한수학회 · 대한수학회보2015 · 제52권 제4호Techniques for computations of the automorphism group of domain변지수영남수학회 · East Asian Mathematical Journal2012 · 제28권 제3호A bounded Kohn Nirenberg domainSimone Calamai대한수학회 · 대한수학회보2014 · 제51권 제5호Affine homogeneous domains in the complex plane이강혁강원경기수학회 · 한국수학논문집2022 · 제30권 제4호An Intrinsic Criterion for the Type of Automorphisms of the Unit Disc이강혁영남수학회 · East Asian Mathematical Journal2021 · 제37권 제3호Perturbation of domains and automorphism groupsBuma L. Fridman, Daowei Ma대한수학회 · 대한수학회지2003 · 제40권 제3호

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