Related papers: Removable singularities for H\"older continuous qu…
Given a semialgebraic set-valued map $F \colon \mathbb{R}^n \rightrightarrows \mathbb{R}^m$ with closed graph, we show that the map $F$ is Holder metrically subregular and that the following conditions are equivalent: (i) $F$ is an open map…
We characterize the removability of H\"older-$\alpha$ graphs with respect to continuous Sobolev $W^{1,2}$ functions. For $\alpha > 2/3$ these graphs are removable, while for $\alpha <2/3$ there exist graphs which are not removable.
We study the problem of removable singularities for degenerate elliptic equations. Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed…
The author has recently introduced the class of CNED sets in Euclidean space, generalizing the classical notion of NED sets, and shown that they are quasiconformally removable. A set $E$ is CNED if the conformal modulus of a curve family is…
We prove a Painlev\'e theorem for bounded quasiregular curves in Euclidean spaces extending removability results for quasiregular mappings due to Iwaniec and Martin. The theorem is proved by extending a fundamental inequality for volume…
For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…
In this paper, we obtain an improved H\"older regularity for quasiregular gradient mappings which was studied by Baernstein and Kovalev.
The present paper is devoted to the study of mappings with finite distortion on Riemannian manifolds. Theorems on local behavior of generalized quasiisometries with unbounded characteristic of quasiconformality are obtained.
We establish the optimal regularity for the distortion of inverses of mappings of finite distortion with logarithm-iterated style subexponentially integrable distortion, which generalizes the Theorem 1. of [J. Gill, Ann. Acad. Sci. Fenn.…
We show that if the maximum modulus of a quasiregular mapping f grows sufficiently rapidly then there exists a non-empty escaping set I(f) consisting of points whose forward orbits under iteration tend to infinity. This set I(f) has an…
We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential…
We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.
We show the possible Milnor numbers of deformations of semi-quasi-homogeneous isolated plane curve singularities. In Theorem 1.1 we list integers can be attained as Milnor numbers of a given semi-quasi-homogeneous singularity.
We give an example of a totally disconnected set E in R^3 which is not removable for quasiconformal homeomorphisms, i.e., there is a homeomorphism f of R^3 to itself which is quasiconformal off E, but not quasiconformal on all of R^3. The…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
By using Moser's iteration technique, we show some removable singularity theorem of the tension field for biharmonic maps into manifolds of non-positive curvature, and the bubbling theorem of biharmonic maps and also harmonic maps.
We extend a well-known theorem by Jones and Makarov [JM] on the singularity of boundary distortion of planar conformal mappings. We use a different technique to recover the previous result and, moreover, generalize the result for…
In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…
We prove existence and uniqueness of an unstable manifold for a degenerate hyperbolic map of the plane arising in statistics.
It is well known that sets of $p$-capacity zero are removable for bounded $p$-harmonic functions, but on metric spaces there are examples of removable sets of positive capacity. In this paper, we show that this can happen even on unweighted…