Related papers: On polyharmonic univalent mappings

We study classes of locally biholomorphic mappings defined in the $\P$ that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations…

We initiate a program aimed at classifying thick ideals, Balmer spectra, and submodule categories of various stable categories of bimodules and modules for finite dimensional selfinjective algebras, and at clarifying the relationship…

We call indexed-biharmonic maps, the solutions of a particular non linear elliptic PDE of order 4. This is a generalization of harmonic maps which verifies that biharmonic maps are biharmonic of index 0. The goal of this article is to study…

Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces.

Recent work of M. Yoshinaga shows that in some instances certain higher homotopy groups of arrangements map onto non-resonant homology. This is in contrast to the usual Hurewicz map to untwisted homology, which is always the zero…

We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class…

Pseudo horizontally weakly conformal maps extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find in this larger class critical points for the (generalized) Faddeev-Hopf energy. Their stability is also…

We show that $X^\lambda$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $\lambda$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the…

First of all, we establish compactness of continuous mappings of the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with the Calderon type condition on $\varphi$ and, in particular, of the Sobolev classes $W^{1,p}_{\rm loc}$ for $p>n-1$…

The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right half-plane mapping or a normalized vertical strip mapping is convex in the direction of the real axis.…

We study the problem of classifying the holomorphic $(m,n)$-subharmonic morphisms in complex space. This determines which holomorphic mappings preserves $m$-subharmonicity in the sense that the composition of the holomorphic mapping with a…

Combining results of Wahl, Galatius--Madsen--Tillmann--Weiss and Korkmaz one can identify the homotopy-type of the classifying space of the stable non-orientable mapping class group $N_\infty$ (after plus-construction). At odd primes p, the…

We establish rigidity results for holomorphic mappings and plurisubharmonic functions in complex geometry. First, under mild conditions, we show that the gradient of a $\operatorname{U}(1)$-invariant strictly plurisubharmonic function in…

We define Hardy spaces $\mathcal{H}^p$ for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

For a K\"{a}hler manifold endowed with a weighted measure $e^{-f}\,dv,$ the associated weighted Hodge Laplacian $\Delta _{f}$ maps the space of $(p,q)$-forms to itself if and only if the $(1,0)$-part of the gradient vector field $\nabla f$…

We study a family of polynomials which are orthogonal with respect to the varying, highly oscillatory complex weight function $e^{ni\lambda z}$ on $[-1,1]$, where $\lambda$ is a positive parameter. This family of polynomials has appeared in…

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain…

We study the asymptotics as $p\uparrow 2$ of stationary $p$-harmonic maps $u_p\in W^{1,p}(M,S^1)$ from a compact manifold $M^n$ to $S^1$, satisfying the natural energy growth condition $$\int_M|du_p|^p=O(\frac{1}{2-p}).$$ Along a…

We present a family of sense-preserving harmonic mappings in the unit disk related to the classical generalized (analytic) Koebe functions. We prove that these are precisely the mappings that maximize simultaneously the real part of every…