$\boldsymbol{\text{C}}^n$中紧齐性强拟凸超曲面的分类
Classification of compact homogeneous strongly pseudoconvex hypersurfaces in $\mathbb C^n$
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中文总结 AI 辅助
本文通过构造显式整映射，将Isaev的实现结果扩展至所有$t>1$，证明例外Morimoto--Nagano模型$M_t^3$可实现为$\boldsymbol{\text{C}}^3$中的紧实解析超曲面，解决了相关长期悬而未决的分类问题。
中文摘要 AI 辅助
通过构造显式整映射，我们证明每个例外Morimoto--Nagano模型$M_t^3$（$t>1$）均可实现为$\boldsymbol{\text{C}}^3$中的紧实解析超曲面。这将Isaev的实现结果从受限参数范围扩展至所有$t>1$，并为Morimoto--Nagano分类中一个长期悬而未决的问题提供了完整解答，该分类针对复欧氏空间中紧单连通实解析超曲面，其在连通李群的CR自同构作用下齐性。
英文摘要
By constructing explicit entire maps, we prove that every exceptional Morimoto--Nagano model $M_t^3$, $t>1$, can be realized as a compact real-analytic hypersurface in $\mathbb C^3$. This extends Isaev's realization results from restricted parameter ranges to all $t>1$ and provides a complete solution to a long-standing open problem in the Morimoto--Nagano classification of compact, simply connected, real-analytic hypersurfaces in complex Euclidean spaces that are homogeneous under the action of a connected Lie group of CR automorphisms.
