Quasiregular mappings and cohomology.

DOI10.1007/BF02401840zbMath1088.30011MaRDI QIDQ5953841

Juha Heinonen, Mario Bonk

Publication date: 2001

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: http://www.actamathematica.org/fulltext.htm

zbMATH Keywords

quasiregular mappingoriented Riemannian manifolds

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) de Rham theory in global analysis (58A12) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (27)

Quasiregular mappings on sub-Riemannian manifolds ⋮ Quasiregular mappings to generalized manifolds ⋮ Asymptotically holomorphic methods for infinitely renormalizable unimodal maps ⋮ Signed quasiregular curves ⋮ Normal families and quasiregular mappings ⋮ Branched covering simply connected 4-manifolds ⋮ In memoriam: Lawrence Allen Zalcman (1943--2022) ⋮ Bubbling of quasiregular maps ⋮ On the nonexistence of certain branched covers ⋮ Slow mappings of finite distortion ⋮ Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion ⋮ Slow quasiregular mappings and universal coverings ⋮ Equilibrium measures for uniformly quasiregular dynamics ⋮ Spaces of differential forms and mappings with controlled distortion ⋮ Rescaling principle for isolated essential singularities of quasiregular mappings ⋮ Bloch's principle ⋮ Mappings of bounded mean distortion and cohomology ⋮ Pull-back of metric currents and homological boundedness of BLD-elliptic spaces ⋮ Conformally formal manifolds and the uniformly quasiregular non-ellipticity of \((\mathbb{S}^2 \times\mathbb{S}^2)\#(\mathbb{S}^2\times\mathbb{S}^2)\) ⋮ On \(p\)-harmonic mappings in the plane ⋮ Quasiregular mappings from a punctured ball into compact manifolds ⋮ A bound on the cohomology of quasiregularly elliptic manifolds ⋮ Entropy in uniformly quasiregular dynamics ⋮ Quasiregular curves of small distortion in product manifolds ⋮ Branched coverings of CP2 and other basic 4‐manifolds ⋮ Finite Distortion Sobolev Mappings between Manifolds are Continuous ⋮ Three-spheres theorem for \(p\)-harmonic mappings

Cites Work

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• Averages of the counting function of a quasiregular mapping
• On the number of omitted values of entire quasiregular mappings
• Curvature, diameter and Betti numbers
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Regularity for a class of nonlinear elliptic systems
• Harmonic functions on manifolds
• Integral estimates for null Lagrangians
• Nonlinear Hodge theory on manifolds with boundary
• Quasiregular mappings in even dimensions
• The analogue of Picard's theorem for quasiregular mappings in dimension three
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• Analytical foundations of the theory of quasiconformal mappings in R^n
• Normal Families of Quasimeromorphic Mappings
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Normal families: New perspectives
• L p Theory of Differential Forms on Manifolds
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Harnack inequality and hyperbolicity for subelliptic \(p\)-Laplacians with applications to Picard type theorems
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