Related papers: Tight maps and holomorphicity
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group which is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the ``analytically…
The class of coarsely convex spaces is a coarse geometric analogue of the class of nonpositively curved Riemannian manifolds. It includes Gromov hyperbolic spaces, CAT(0) spaces, proper injective metric spaces and systolic complexes. It is…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
The work is motivated by the papers [Ba1], [Ba2], [Ba7], [Ba11], [Be] and [Be-Tu]. In particular, the strong homology groups of continuous maps were defined and studied in [Be] and [Be-Tu]. To show that given groups are homology type…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
On non-K\"ahler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of…
We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of `quantum thick morphisms' defined here as particular oscillatory integral operators on functions.
We construct explicit examples of $p$-harmonic maps $u:\mathbb{R}^n \to \mathbb{R}^N$. These are more irregular than the previously known examples and thus provide new upper bounds for the regularity of $p$-harmonic maps, including the case…
We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type we show that…
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the…
We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can…
We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single…
In the early 1980's Thurston gave a topological characterization of rational maps whose critical points have finite iterated orbits (\cite{Th,DH1}): given a topological branched covering $F$ of the two sphere with finite critical orbits, if…
A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the…
In this short work we prove that the Hilbert Grassmannians endowed with the weak topology are models for the classifying spaces of the unitary groups. As application of this result one can use Hilbert Grassmannians for the presentation of…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
Higher order group cohomology is defined and first properties are given. Using modular symbols, an Eichler-Shimura homomorphism is constructed mapping spaces of higher order cusp forms to higher order cohomology groups.
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…
We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichm\"uller space, we consider whether they are quasi-isometric embeddings with respect to…