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<p>We proved that a map on bounded balanced pseudoconvex domainswhose Shilov boundaries are transitive under the isotropy groups of 0 isCarathéodory extremal map if and only if it is the extremal map of the squeezingfunction at the origin, and we also obtain the formulas of these two extremal mapswhich are unique up to unitary linear transformations. Especially, all of these twoextremal maps are non-singular linear transformations. Then we generalize theabove results to balanced domains with center at nonzero points.</p>

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The relationship between Carathéodory and squeezing extremal maps on bounded balanced pseudoconvex domains

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • C. Zhong,
  • A. Wang

摘要

We proved that a map on bounded balanced pseudoconvex domainswhose Shilov boundaries are transitive under the isotropy groups of 0 isCarathéodory extremal map if and only if it is the extremal map of the squeezingfunction at the origin, and we also obtain the formulas of these two extremal mapswhich are unique up to unitary linear transformations. Especially, all of these twoextremal maps are non-singular linear transformations. Then we generalize theabove results to balanced domains with center at nonzero points.