On Value Distributions for Quasimeromorphic Mappings on $\mathbb H$-type Carnot Groups

Sobolev mappings and moduli inequalities on Carnot groups

In the article we study mappings of Carnot groups satisfy moduli inequalities. We prove that homeomorphisms satisfy the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem we prove that mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W^1_{ν,\text{loc}}(Ω;Ω')$ belong to the Sobolev class $W^1_{1,\text{loc}}(Ω';Ω)$.

The Subelliptic $\infty$-Laplace System on Carnot-Carathéodory Spaces

Given a Carnot-Carathéodory space $\Om \sub \R^n$ with associated vector fields $X=\{X_1,...,X_m\}$, we derive the subelliptic $\infty$-Laplace system for mappings $u : \Om \larrow \R^N$, which reads \[ \label{1} \De^X_\infty u \, :=\, \Big(Xu \ot Xu + \|Xu\|^2 [Xu]^\bot \ot I \Big) : XX u\, = \, 0 \tag{1} \] in the limit of the subelliptic $p$-Laplacian as $p\ri \infty$. Here $Xu$ is the horizontal gradient and $[Xu]^\bot$ is the projection on its nullspace. Next, we identify the Variational Principle characterizing \eqref{1}, which is the "Euler-Lagrange PDE" of the supremal functional \[ \l…

Reshetnyak类映射与复合算子

Reshetnyak-class mappings and composition operators

本文研究了Carnot群中Reshetnyak类同胚的等价描述，通过诱导有界复合算子刻画映射性质，提供了更简短的新证明并揭示了同胚的新特性。

欧几里得空间中的Sobolev映射与积结构

Sobolev mappings of Euclidean space and product structure

研究证明在 $n \ge 2$ 时，满足特定条件的 Sobolev 映射必须分裂，但 $n=1$ 时这一结论不成立，且与之前工作相补充。