Search results for "ta111"

$n$-harmonic coordinates and the regularity of conformal mappings

2014

This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with $C^r$ metric tensors ($r > 1$) is a $C^{r+1}$ conformal (local) diffeomorphism. This result was proved in [12, 27, 33], but we give a new proof of this fact. The proof is based on $n$-harmonic coordinates, a generalization of the standard harmonic coordinates that is particularly suited to studying conformal mappings. We establish the existence of a $p$-harmonic coordinate system for $1 < p < \infty$ on any Riemannian manifold.

Conformality and $Q$-harmonicity in sub-Riemannian manifolds

2016

We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.

A note on Sobolev isometric immersions below W2,2 regularity

2017

Abstract This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W 2 , 2 setting. We show that the Hessian of each coordinate function of a W 2 , p , p 2 , isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W 2 , p , p 2 , isometric immersion from a bounded domain of R 2 into R 3 that has multiple singularities.

Boundary Behavior of Harmonic Functions on Gromov Hyperbolic Manifolds

2013

Isoperimetric inequality from the poisson equation via curvature

2012

In this paper, we establish an isoperimetric inequality in a metric measure space via the Poisson equation. Let (X,d,μ) be a complete, pathwise connected metric space with locally Ahlfors Q-regular measure, where Q > 1, that supports a local L2-Poincare inequality. We show that, for the Poisson equation Δu = g, if the local L∞-norm of the gradient Du can be bounded by the Lorentz norm LQ,1 of g, then we obtain an isoperimetric inequality and a Sobolev inequality in (X,d,μ) with optimal exponents. By assuming a suitable curvature lower bound, we establish such optimal bounds on . © 2011 Wiley Periodicals, Inc.

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.

Patterns of trading profiles at the Nordic Stock Exchange. A correlation-based approach.

2016

We investigate the trading behavior of Finnish individual investors trading the stocks selected to compute the OMXH25 index in 2003 by tracking the individual daily investment decisions. We verify that the set of investors is a highly heterogeneous system under many aspects. We introduce a correlation based method that is able to detect a hierarchical structure of the trading profiles of heterogeneous individual investors. We verify that the detected hierarchical structure is highly overlapping with the cluster structure obtained with the approach of statistically validated networks when an appropriate threshold of the hierarchical trees is used. We also show that the combination of the cor…

The origin of in-plane stresses in axially moving orthotropic continua

2016

In this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in th…

Mappings of exponentially integrable distortion: Decay of the Jacobian

2018

We establish an integrability result on the reciprocal of the Jacobian determinant for a mapping of exponentially integrable distortion and thus answer a question raised by S. Hencl and P. Koskela.

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.