Quasiregular maps on Carnot groups

DOI10.1007/BF02921707zbMath0905.30018MaRDI QIDQ1130259

Ilkka Holopainen, Juha Heinonen

Publication date: 20 August 1998

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Heisenberg groupCarnot groupsnonlinear potential theoryquasiregular maps

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Elliptic equations on manifolds, general theory (58J05) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (41)

Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings ⋮ On the smoothness of $C^1$-contact maps in $C^\infty$-rigid Carnot groups ⋮ Quasiregular mappings on sub-Riemannian manifolds ⋮ Strong comparison principle for 𝑝-harmonic functions in Carnot-Caratheodory spaces ⋮ ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP ⋮ On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups ⋮ POINCARÉ AND SOBOLEV INEQUALITIES FOR DIFFERENTIAL FORMS IN HEISENBERG GROUPS AND CONTACT MANIFOLDS ⋮ Conformality and \(Q\)-harmonicity in Carnot groups ⋮ Unnamed Item ⋮ \(p\)-harmonic functions in the Heisenberg group: boundary behaviour in domains well-approximated by non-characteristic hyperplanes ⋮ Sharp capacity estimates for annuli in weighted \(\mathbf {R}^n\) and in metric spaces ⋮ Stability theorems for H-type Carnot groups ⋮ On the radial limits of mappings on Riemannian manifolds ⋮ Openness and discreteness of mappings of finite distortion on Carnot groups ⋮ Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group ⋮ Hardy-Sobolev type inequalities with sharp constants in Carnot-Carathéodory spaces ⋮ Boundary behavior of mappings in \(\lambda(\epsilon)\)-regular metric spaces ⋮ Fundamental solution for the \(Q\)-Laplacian and sharp Moser--Trudinger inequality in Carnot groups. ⋮ Mappings with bounded \((P,Q)\)-distortion on Carnot groups ⋮ Boundary behavior of \(p\)-harmonic functions in the Heisenberg group ⋮ On the Lie algebra of polarizable Carnot groups ⋮ Mappings with bounded distortion and with finite distortion on Carnot groups ⋮ Generalizations of a Laplacian-type equation in the Heisenberg group and a class of Grushin-type spaces ⋮ Modules of systems of measures on polarizable Carnot groups ⋮ Uniformly quasiregular maps on the compactified Heisenberg group ⋮ Metric and geometric quasiconformality in Ahlfors regular Loewner spaces ⋮ \(L^q\)-\(L^\infty\) Hölder continuity for quasilinear parabolic equations associated to Sobolev derivations ⋮ \(p\)-module of vector measures in domains with intrinsic metric on Carnot groups ⋮ Sharp weighted Young's inequalities and Moser-Trudinger inequalities on Heisenberg type groups and Grushin spaces ⋮ Equivalence of weak and viscosity solutions to the \({\mathtt{p}}(x)\)-Laplacian in Carnot groups ⋮ Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces ⋮ Hardy-Littlewood inequality for quasiregular maps on Carnot groups ⋮ The morphism property of subelliptic equations on the roto-translation group ⋮ Starshapedeness for fully non‐linear equations in Carnot groups ⋮ Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type ⋮ The morphism property for mappings with bounded distortion on the Heisenberg group ⋮ On mappings with bounded distortion on Heisenberg group ⋮ Cluster sets theorems on metric measure spaces ⋮ Quasilinear equations with source terms on Carnot groups ⋮ Improved critical Hardy inequality and Leray-Trudinger type inequalities in Carnot groups ⋮ Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type

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