Search results for "math.CV"
showing 10 items of 55 documents
Improved Hölder regularity for strongly elliptic PDEs
2019
We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H\"older regularity, higher than what is given by the classical exponent $1/K$.
Intrinsic Hardy–Orlicz spaces of conformal mappings
2014
We define a new type of Hardy-Orlicz spaces of conformal mappings on the unit disk where in place of the value |f(x)| we consider the intrinsic path distance between f(x) and f(0) in the image domain. We show that if the Orlicz function is doubling then these two spaces are actually the same, and we give an example when the intrinsic Hardy-Orlicz space is strictly smaller.
Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion
2010
We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.
Quasiregular ellipticity of open and generalized manifolds
2014
We study the existence of geometrically controlled branched covering maps from \(\mathbb R^3\) to open \(3\)-manifolds or to decomposition spaces \(\mathbb {S}^3/G\), and from \(\mathbb {S}^3/G\) to \(\mathbb {S}^3\).
Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps
2018
The image of the branch set of a piecewise linear (PL)‐branched cover between PL 𝑛n‐manifolds is a simplicial (𝑛−2)(n−2)‐complex. We demonstrate that the reverse implication also holds: an open and discrete map 𝑓:𝕊𝑛→𝕊𝑛f:Sn→Sn with the image of the branch set contained in a simplicial (𝑛−2)(n−2)‐complex is equivalent up to homeomorphism to a PL‐branched cover. peerReviewed
On proper branched coverings and a question of Vuorinen
2022
We study global injectivity of proper branched coverings from the open Euclidean n$n$-ball onto an open subset of the Euclidean n$n$-space in the case where the branch set is compact. In particular, we show that such mappings are homeomorphisms when n=3$n=3$ or when the branch set is empty. This gives a positive answer to the corresponding cases of a question of Vuorinen. Peer reviewed
A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group
2017
We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group $\mathbb{H}_1$. Several auxiliary properties of quasiconformal mappings between subdomains of $\mathbb{H}_1$ are proven, including distortion of balls estimates and local BMO-estimates for the logarithm of the Jacobian of a quasiconformal mapping. Applications of the Koebe theorem include diameter bounds for images of curves, comparison of integrals of the average derivative and the operator norm of the horizontal differential, as well as the study of quasiconformal densities and metrics in domains in $\mathbb{H}_1$. The theorems are discussed for…
Uniformization of metric surfaces using isothermal coordinates
2021
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct suitable isothermal coordinates.
Conformal equivalence of visual metrics in pseudoconvex domains
2017
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between pseudoconvex domains. The proofs are inspired by Mostow's proof of his rigidity theorem and are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the Bonk-Schramm hyperbolic fillings.
Equivalence of quasiregular mappings on subRiemannian manifolds via the Popp extension
2016
We show that all the common definitions of quasiregular mappings $f\colon M\to N$ between two equiregular subRiemannian manifolds of homogeneous dimension $Q\geq 2$ are quantitatively equivalent with precise dependences of the quasiregularity constants. As an immediate consequence, we obtain that if $f$ is $1$-quasiregular according to one of the definitions, then it is also $1$-quasiregular according to any other definition. In particular, this recovers a recent theorem of Capogna et al. on the equivalence of $1$-quasiconformal mappings. Our main results answer affirmatively a few open questions from the recent research. The main new ingredient in our proofs is the distortion estimates for…