C^4中均匀管畴的分类

Rossi地图和E.齐次强伪凸三维超曲面的Cartan分类

Analogues of Rossi's map and E. Cartan's classification of homogeneous strongly pseudoconvex 3-dimensional hypersurfaces

我们介绍了由于Rossi的映射的类似物，并展示了它们如何被用来明确地确定某些齐次强伪凸三维超曲面的所有覆盖，这些超曲面出现在E. 1932年的卡尔丹。

紧致齐次流形上的复结构和Kaehler结构--它们的存在性、分类和模问题

Complex and Kaehler structures on compact homogeneous manifolds - their existence, classification and moduli problem

紧致流形上某些复杂几何结构的存在，如复结构、Kaehler（伪Kaehler）结构等，往往对它的拓扑流形或微分流形有一定的限制.本文综述了紧致齐性流形上这类结构的存在性、分类和模问题的研究进展。

Continuing the classification of homogeneous Kobayashi-hyperbolic manifolds with high-dimensional automorphism group

We classify all homogeneous Kobayashi-hyperbolic manifolds of dimension $n \ge 2$ whose group of holomorphic automorphisms has dimension either $n^2 - 7$ or $n^2 - 8.$ This paper continues the work of A. Isaev, who classified all such manifolds with automorphism group dimension $n^2 - 6$ and greater.

超二次曲面到对称形式零锥上的管状域的CR映射分类

The classification of CR maps from hyperquadrics into tubes over null cones of symmetric forms

本文分类了从超二次曲面到对称形式零锥管状域的CR映射，发现新等价类并证明高维情形下映射延拓为不定Kähler度量的局部等距，同时给出广义单位球到广义Lie球的真映射分类。

Cohomological Laplace transform on non-convex cones and Hardy spaces of $\bar{\partial}$-cohomology on non-convex tube domains

We consider a class of non-convex cones $V$ in $\mathbb{R}^n$ which can be presented as (not unique) union of convex cones of some codimension $q$ which we call the index of non-convexity. This class contains non-convex symmetric homogeneous cones studied by the first author and his collaborators. For these cones we consider a construction of dual non-convex cones $V^*$ and corresponding non-convex tubes $T$ and define a cohomological Laplace transform from functions at $V$ to $q$-dimensional cohomology of $T$ using the language of smoothly parameterized uCech cohomology. We give a constructio…

Classification of homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$

Locally homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^2$ were classified by E.\,Cartan in 1932. In this work, we complete the classification of locally homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$.

Holomorphic Function Spaces on Homogeneous Siegel Domains

We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object of our study concerns weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. These problems include: sampling, atomic decomposition, duality, boundary values, boundedness of the Bergman projectors. Our analysis include the Hardy spaces, and suitable generalizations of the classical Bloch and Dirichlet spaces. One of the main novelties in this work is the generality of the domains under consideration, that is, homogeneous Siegel domains, extending many results …

5维Levi退化齐次CR-流形的分类

Classification of Levi degenerate homogeneous CR-manifolds in dimension 5

本文给出了5维齐次2-非退化CR-流形的新例子，并在局部CR-等价的条件下，给出了这类CR-流形的一个完全分类。

On CR maps from the sphere into the tube over the future light cone

We determine all local smooth or formal CR maps from the unit sphere $\mathbb{S}^3\subset \mathbb{C}^2$ into the tube $\mathcal{T}:= \mathcal{C} \times i\mathbb{R}^3 \subset \mathbb{C}^3$ over the future light cone $\mathcal{C}:= \left\{x\in \mathbb{R}^3\colon x_1^2+x_2^2 = x_3^2, \ x_3 > 0\right\}$. This result leads to a complete classification of proper holomorphic maps from the unit ball in $\mathbb{C}^2$ into Cartan's classical domain of type IV in $\mathbb{C}^3$ that extend smoothly to some boundary point. Up to composing with CR automorphisms of the source and target, the classification…

非紧二维Kaehler齐性流形的分类

Classification of Kaehler homogeneous manifolds of non-compact dimension two

设$G$是一个连通复李群，$H$是一个闭复子群，使得$X := G/H$是Kaehler，且系数在$\mathbb Z_2$中的$X$的上非零同调群的余维数小于或等于2.我们证明了$X$是双全纯的一个复杂的齐次流形构造使用众所周知的基本积木，即，$\mathbb C, \mathbb C^*$、Cousin群和旗流形。

四维齐次CR-流形的分类

Classification of homogeneous CR-manifolds in dimension 4

E. Cartan对3维局部齐次CR-流形进行了分类，直到局部CR-等价。我们分类，直到局部CR-等价，所有局部齐次CR-流形在4维。分类定理也使我们能够分类所有对称CR流形在4维，直到当地双全纯等价。我们还证明了任何4维实李代数都可以实现为$\CC{3}$中某个区域上的仿射向量场的代数，并且在每一点上都是线性无关的。

有理齐性空间嵌入Nilpotent轨道的等变Legendrian分类

Classification of Equivariant Legendrian Embeddings of Rational Homogeneous Spaces into Nilpotent Orbits

本文研究了有理齐性空间到adjoint种的等变Legendrian嵌入分类，通过分析Nilpotent轨道的复接触结构，提出了一种基于稳定子群作用的齐性子变种分类方法。

关于复空间中齐次超曲面的分类

On the Classification of Homogeneous Hypersurfaces in Complex Space

本文讨论了复仿射$n$ -维二次曲面中的实超曲面族$M_t^n$，其中$n\ge 2$，$t>1$是由Morimoto和Nagano在${\mathbb C}^n$中对齐次紧致单连通实解析超曲面的分类而产生的。为了最终确定它们的分类，需要解决$M_t^n$在$n=3,7$的${\mathbb C}^n$中的可嵌入性问题。我们发现，$M_t^7$是不嵌入在${\mathbb C}^7$的每一个$t$和$M_t^3$是嵌入在${\mathbb C}^3$的所有$1<t<1+10^{-6}$。由于我们的分析的地图所构建的Ahern和Rudin，我们还推测，嵌入的$M_t^3$发生的所有\，$1<t<\sqrt{(2+\sqrt{2})/3}$。

$\mathbb C^2$中对称超曲面的局部等价性

Local equivalence of symmetric hypersurfaces in $\mathbb C^2$

有限型超曲面上的Chern-Moser标准形及其类似形式一般不尊重对称性。推广了N. K. Stanton，我们考虑了$\mathbb C^2$中有限型对称Levi退化超曲面的局部等价问题.结果给出了所有这样的超曲面的一个完整的正规化，尊重对称性。特别是，它们适用于管和刚性超曲面，提供了一个有效的分类。主要工具是为具有管模型的一般超曲面构造完全规范形。作为应用，我们描述了所有管间的双全纯映射，回答了N。韩吉斯

$\boldsymbol{\text{C}}^n$中紧齐性强拟凸超曲面的分类

Classification of compact homogeneous strongly pseudoconvex hypersurfaces in $\mathbb C^n$

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。