Related papers: Remarks on Martio's conjecture

We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.

We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot…

We construct an a.e. approximately differentiable homeomorphism of a unit $n$-dimensional cube onto itself which is orientation preserving, has the Lusin property (N) and has the Jacobian determinant negative a.e. Moreover, the…

We prove a characterization result in the spirit of the Kinderlehrer-Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is the pointwise Jacobian is positive…

In terms of dilatations, it is proved a series of criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between regular domains on the Riemann surfaces

In this short note, we consider quasiregular local homeomorphisms on uniform domains. We prove that such mappings always can be extended to some boundary points along John curves, which extends the corresponding result of Rajala [Amer. J.…

In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable…

The paper is devoted to the study of mappings with non--bounded characteristics of quasiconformality. The analog of the theorem about radius injectivity of locally quasiconformal mappings was proved for some class of mappings. There are…

We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced in [12], sufficient to guarantee the extendability of a conformal map f from the unit disk…

We consider polynomial maps of affine space over an algebraically closed field of characteristic zero. We prove that every irreducible component of the zero locus of the Jacobian determinant corresponds to either a contracted divisor or a…

We prove two-sided inequalities for the $L^p$-norm of a pushforward or pullback (with respect to an orientation-preserving diffeomorphism) on oriented volume and Riemannian manifolds. For a function or density on a volume manifold, these…

Let $m \geqslant 6$ be an even integer. In this short note we prove that the Jacobian variety of a quasiplatonic Riemann surface with associated group of automorphisms isomorphic to $C_2^2 \rtimes_2 C_m$ admits complex multiplication. We…

This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian…

We consider quasiconformal mappings of the unit disk that have a planar extension which have $p$-integrable distortion. In this paper, we establish a bound for the modulus of continuity for the inverse mapping and show sharpness of this…

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…

We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian…

We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$, i.e. bi-Sobolev solutions for the prescribed Jacobian inequality in the plane for right-hand sides $f\in…

Let $F\in W^{1,n}_{\text{loc}}(\Omega; \Bbb R^n)$ be a mapping with nonnegative Jacobian $J_F(x)=\det DF(x)\ge 0$ for a.e. $x$ in a domain $\Omega\subset\Bbb R^n$. The {\it dilatation} of $F$ is defined (almost everywhere in $\Omega$) by…

We study mappings differentiable almost everywhere, possessing the $N$-Luzin property, the $ N^{\,-1}$-property on the spheres with respect to the $(n-1)$-dimensional Hausdorff measure and such that the image of the set where its Jacobian…

Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational…