A Lipschitz version of de Rham theorem for $L_p$-cohomology

TL;DR

This paper develops a Lipschitz version of the de Rham theorem for $L_p$-cohomology, extending classical results to metric simplicial complexes with bounded geometry using regularization techniques.

Contribution

It introduces a Lipschitz de Rham calculus framework for $L_p$-cohomology on metric complexes, providing new tools for geometric analysis.

Findings

Establishes a Lipschitz de Rham theorem for $L_p$-cohomology.

Applies regularization techniques to metric simplicial complexes.

Extends classical de Rham results to Lipschitz and metric settings.

Abstract

We focus our attention on the de Rham operators' underlying properties which are specified by intrinsic effects of differential geometry structures. And then we apply the procedure of regularization in the context of Lipschitz version of de Rham calculus on metric simplicial complexes with bounded geometry.