Euclidean domains in complex manifolds

Embedding almost-complex manifolds in almost-complex Euclidean spaces

We show that any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m) equipped with a suitable almost-complex structure.

Isometric and CR pluriharmonic immersions of three dimensional CR manifolds in Euclidean spaces

Using a bigraded differential complex depending on the CR and pseudohermitian structure, we give a characterization of three-dimensional strongly pseudoconvex pseudo-hermitian CR-manifolds isometrically immersed in Euclidean space $\mathbb{R}^n$ in terms of an integral representation of Weierstrass type. Restricting to the case of immersions in $\mathbb{R}^4$, we study harmonicity conditions for such immersions and give a complete classification of CR-pluriharmonic immersions.

复球面 bundle 与复欧几里得空间之间的凯勒子流形

The Kähler submanifolds between the ball bundles and the complex Euclidean space

本文研究复球面 bundle 与复欧几里得空间之间凯勒子流形的不存在性，提出充分条件并给出若干类球面 bundle 的不存在定理。

闭拟正则椭圆流形的 de Rham 代数是欧几里得的

De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean

本文证明接受从 $\mathbb R^n$ 出发的非常值拟正则映射的闭定向流形，其 de Rham 上同调代数可嵌入外代数，并据此分类闭单连通拟正则椭圆 $4$-流形。

On embeddings of almost complex manifolds in almost complex Euclidean spaces

We prove that any compact almost complex manifold $(M, J)$ of real dimension $2m$ admits a pseudo-holomorphic embedding in a Euclidean space of dimension $4m + 2$, endowed with a suitable non-standard almost complex structure. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class of $(M, J)$, for the existence of an embedding or an immersion in an almost complex Euclidean $4m$-space. We also discuss the pseudo-holomorphic embeddings of an almost complex 4-manifold in $R^6$.

从具有受控几何的广义n维流形获得准正则值

Quasiregular values from generalized manifold with controlled geometry

本文在广义n维流形与欧几里得空间之间建立准正则值的Reshetnyak定理，扩展了Kangasniemi和Onninen之前在欧几里得空间中的研究成果。