Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings
From MaRDI portal
Publication:4961514
zbMath1402.30031arXiv1512.09165MaRDI QIDQ4961514
Tomasz Adamowicz, Ben Warhurst
Publication date: 25 October 2018
Full work available at URL: https://arxiv.org/abs/1512.09165
Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Cluster sets, prime ends, boundary behavior (30D40) Quasiconformal mappings in metric spaces (30L10)
Related Items
Hardy spaces and quasiconformal maps in the Heisenberg group, On boundary extension of mappings in metric spaces in the terms of prime ends, Carathéodory-type extension theorem with respect to prime end boundaries, The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Prime ends for domains in metric spaces
- Nonlinear potential theory on metric spaces
- Uniformly quasiregular maps on the compactified Heisenberg group
- Extremal length and functional completion
- Conformality and \(Q\)-harmonicity in Carnot groups
- An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
- Quasiconformal mappings on the Heisenberg group
- Geometric properties of Heisenberg-type groups
- Uniform domains
- Quasiconformal maps of cylindrical domains
- Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
- Quasiregular maps on Carnot groups
- Prime ends and quasiconformal mappings
- On the existence of angular limits of \(n\)-dimensional quasiconformal mappings
- John disks
- Quasiconformal maps in metric spaces with controlled geometry
- Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics
- On coincidence of \(p\)-module of a family of curves and \(p\)-capacity on the Carnot group.
- Polar coordinates in Carnot groups
- Lectures on analysis on metric spaces
- Sobolev classes of Banach space-valued functions and quasiconformal mappings
- Foundations for the theory of quasiconformal mappings on the Heisenberg group
- \(H\)-type groups and Iwasawa decompositions
- Régularité d'accès des bouts et frontière de Martin d'un domaine euclidiens
- Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
- Decomposition of continua and prime ends
- Uniform domains and quasiconformal mappings on the Heisenberg group
- Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations
- Geometry of prime end boundary and the Dirichlet problem for bounded domains in metric measure spaces
- The Dirichlet problem for \(p\)-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities
- The Dirichlet problem for \(p\)-harmonic functions on the topologist's comb
- Extremal length and p-capacity
- Lectures on \(n\)-dimensional quasiconformal mappings
- Beurling's theorem on exceptional sets
- Sets of uniqueness for functions regular in the unit circle
- Metric and geometric quasiconformality in Ahlfors regular Loewner spaces
- Non-conformal Loewner type estimates for modulus of curve families
- Contact and 1-quasiconformal maps on Carnot groups
- Linearly locally connected sets and quasiconformal mappings
- Cluster sets and quasiconformal mappings
- Boundary Values for Some Classes of Functions
- Snowballs are quasiballs
- Stratified Lie Groups and Potential Theory for their Sub-Laplacians
- Rings and Quasiconformal Mappings in Space
- Capacity Densities and Angular Limits of Quasiregular Mappings
- Prime Ends
- Injectivity theorems in plane and space
- Conformal deformations of uniform Loewner spaces
- On Prime Ends and Plane Continua
- Sobolev met Poincaré
- Regular domains in homogeneous groups
- Sobolev Spaces on Metric Measure Spaces
- Extension of Loewner's Capacity Theorem
- Modulus method and radial stretch map in the Heisenberg group
- Enden und Primenden
- Recherches sur la théorie des bouts premiers
- Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group
