• 제목/요약/키워드: Reinhardt domains

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CHARACTERIZATION OF REINHARDT DOMAINS BY THEIR AUTOMORPHISM GROUPS

  • Isaen, Alexander-V.;Krantz, Steven-G.
    • 대한수학회지
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    • 제37권2호
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    • pp.297-308
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    • 2000
  • 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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INVARIANT METRICS AND COMPLETENESS

  • Pflug, Peter
    • 대한수학회지
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    • 제37권2호
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    • pp.269-284
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    • 2000
  • We discuss completeness with respect to the Caratheodory distance, the Kobayashi distance and the Beraman distance, respectively.

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AUTOMORPHISM GROUPS ON CERTAIN REINHARDT DOMAINS

  • Kang, Hyeonbae
    • 대한수학회보
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    • 제30권2호
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    • pp.171-177
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    • 1993
  • In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.

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MAXIMUM MODULI OF UNIMODULAR POLYNOMIALS

  • Defant, Andreas;Garcia, Domingo;Maestre, Manuel
    • 대한수학회지
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    • 제41권1호
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    • pp.209-229
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    • 2004
  • Let $\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $$\mid$s_{\alpha}$\mid$\;=\;1$ for all multi indices $\alpha$), and let $R\;{\subset}\;{\mathbb{C}}^n$ be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;$\mid$\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha}$\mid$$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. $s_{\alpha}\;=\;{\pm}1$ for all multi indices $\alpha$). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.