Quasiregular mappings and 𝒲𝒯 -classes of differential forms on Riemannian manifolds

Abstract

The purpose of this paper is to study the relations between quasiregular mappings on Riemannian manifolds and differential forms. Four classes of differential forms are introduced and it is shown that some differential expressions connected in a natural way to quasiregular mappings are members in these classes.

On quasiplanes in Euclidean spaces

“…Below we use the terminology and notation of [7]. Let R n be the n-dimensional Euclidean space, n ≥ 2, let f : R n → R n be a mapping of the class W If f : R n → R n is quasiconformal, then it is well known that f (R n ) = R n and the inverse map f −1 : R n → R n is also quasiconformal in R n with K(f…”

Weak reverse Hölder inequality of weakly A-harmonic sensors and Hölder continuity of A-harmonic sensors

“…In this section, we establish the Hölder continuity for differential forms satisfying A-harmonic equation (1.1) by isoperimetric inequality for differential forms from [8] and Morrey's Lemma for differential forms in [9]. Let Γ = Γ(a 1 , a 2 ) be the family of locally rectifiable arcs γ ℝ n joining the points a 1 and a 2 .…”

“…Now we give the definition of Hölder continuity for differential forms which appears in [9]. Remark: If the differential form u of degree zero, i.e.…”

Removable Singularities of 𝒲𝒯-Differential Forms and Quasiregular Mappings

“…Our notation is as in [1]. Let ᏹ be a Riemannian manifold of the class C 3 , dimᏹ = n, without boundary.…”