Related papers: Signed quasiregular curves

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…

We show that a $K$-quasiregular $\omega$-curve from a Euclidean domain to a Euclidean space with respect to a covector $\omega$ is locally $(1/K)(\lVert \omega\rVert/|\omega|_{\ell_1})$-H\"older continuous. We also show that quasiregular…

We extend the notion of a pseudoholomorphic vector of Iwaniec, Verchota, and Vogel to mappings between Riemannian manifolds. Since this class of mappings contains both quasiregular mappings and (pseudo)holomorphic curves, we call them…

A hypersurface is said to be quasihomogeneous if in suitable coordinates with assigned weights, its equation becomes weighted homogeneous in its variables. For an irreducible quasihomogeneous plane curve, the equation necessarily becomes a…

Let $N$ be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular $\omega$-curve $\mathbb{R}^n \to N$ with infinite energy. We prove that, if the de Rham class of $\omega$ is non-zero and belongs to a so-called…

In this paper we give a classification of cohomogeneity one manifolds admitting an invariant metric with quasipositive sectional curvature except for two $7$-dimensional families. The main result carries over almost verbatim from the…

Let $f\colon M \to M$ be a uniformly quasiregular self-mapping of a compact, connected, and oriented Riemannian $n$-manifold $M$ without boundary, $n\ge 2$. We show that, for $k \in \{0,\ldots, n\}$, the induced homomorphism $f^* \colon…

We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all…

In this paper we study quasiconformal curves which are a special case of quasiregular curves. Namely embeddings $\Omega\rightarrow\mathbb{R}^m$ from some domain $\Omega\subset\mathbb{R}^n$ to $\mathbb{R}^m$, where $n\leq m$, which belong in…

In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for…

We give a quasihomogeneity criterion for Gorenstein curves. For complete intersections, it is related to the first step of Vasconcelos' normalization algorithm. In the process, we give a simplified proof of the Kunz-Ruppert criterion.

While the equality of differential signatures (Calabi et al, Int. J. Comput. Vis. 26: 107-135, 1998) is known to be a necessary condition for congruence, it is not sufficient (Musso and Nicolodi, J. Math Imaging Vis. 35: 68-85, 2009).…

A quasislit is the image of a vertical line segment [0, iy], y > 0, under a quasiconformal homeomorphism of the upper half-plane fixing infinity. Quasislits correspond precisely to curves generated by the Loewner equation with a driving…

We prove that the recently shown cohomological obstruction for quasiregular ellipticity has a generalization in the theory of quasiregular values. More specifically, if $M$ is a closed, connected, and oriented Riemannian $n$-manifold, and…

We develop the theory of coregular sequences and codepth for modules that need not be finitely generated or artinian over a Noetherian ring. We use this theory to give a new version of a theorem of Hellus characterizing set-theoretic…

An important problem in applications of quasiconformal analysis and in its numerical aspect is to establish algorithms for explicit or approximate determination of the basic quasiinvariant curvelinear and analytic functionals intrinsically…

We investigate space curves with large cohomology. To this end we introduce curves of subextremal type. This class includes all subextremal curves. Based on geometric and numerical characterizations of curves of subextremal type, we show…

Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that…

We show that a closed, connected and orientable Riemannian manifold of dimension $d$ that admits a quasiregular mapping from $\mathbb R^d$ must have bounded cohomological dimension independent of the distortion of the map. The dimension of…

A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in discrete groups, showing that all quasihomomorphisms can be…