# Weakly Lipschitz mappings in higher dimensions

“Weakly Lipschitz mappings in higher dimensions” (2026), by Anatoly Golberg. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Anatoly Golberg
- Published: November 2, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.03532
- Free PDF: https://arxiv.org/pdf/2611.03532

## 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_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.

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