3 papers
math.DG2025
Some Poincaré--Sobolev inequalities for differential forms
Vladimir Gol'dshtein, Yaroslav Kopylov, Roman Panenko
We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Goldshtein and Troyanov. As in this paper, ou…
math.DG2023
On the de Rham homomorphism for -cohomologies
V. Gol'dshtein, R. Panenko
We study the procedure of regularization in the context of the Lipschitz version of de Rham calculus on metric simplicial complexes with bounded geometry. It provides us with the m…
math.DG2022
A Lipschitz version of de Rham theorem for -cohomology
Vladimir Gol'dshtein, Roman Panenko
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…