Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.03532

Weakly Lipschitz mappings in higher dimensions

Anatoly Golberg
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce and investigate the main features of weakly Lipschitz mappings whose pointwise Lipschitz constant is controlled from above by the derivative of a set function. The main results give conditions under which such mappings belong to $W^{1,n}_{\rm loc},$ and show that the class contains metrically quasiconformal mappings as a proper subclass. In addition, under a Rado--Reichelderfer type oscillation assumption, we derive diameter control, image-measure bounds, sufficient conditions for Lusin's $(N)$-property, and an area formula.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anatoly Golberg. 2026-11-02. Weakly Lipschitz mappings in higher dimensions. https://arxiv.org/abs/2611.03532

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Different approach to certain problems in univalent function theory

Using different approach we consider some problems for the class $\mathcal{S}_{ex}^{\star}$ defined by the condition $\frac{zf'(z)}{f(z)}\prec e^{αz}$, $0<α\leq1.$ Our method is more simple than that used by Das and Sarkar in their work: \textit{Sharp coefficient estimates for the exponential starlike class $S^\star_{ex}$} (\cite{DS26}).

math.CV↗
arXiv2026

Local convexity obstructions for bounded realizations of Teichmüller space

Let $D\subset\mathbb{C}^n$, $n\ge2$, be a bounded domain that is biholomorphic to a finite-dimensional Teichmüller space. We prove that $\partial D$ has no locally convex boundary patch containing a complex $(n-1)$-dimensional manifold through each of its points. Note that in complex dimension two this excludes every locally convex boundary point, without any boundary regularity assumption. In every dimension, we also exclude locally convex $C^2$ boundary patches.

math.CV↗