arXiv research

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic $\infty$-harmonic maps from and into a sphere, quadratic $\infty$-harmonic maps between E…

Holomorphic maps between moduli spaces are shown to be forgetful for large g.

The study classifies conformal biharmonic and k-polyharmonic maps between space forms.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.

There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps between the end spaces are translated to some classes of coarse maps (or even c…

In this paper are studied the harmonic maps between two generalized Lagrange spaces. At the same time, it is proved that the solutions of $C^2$ class of certain ODEs or PDEs are harmonic maps between certain convenient generalized Lagrange spaces.

This paper extends boundary embedding results to coarsely convex spaces.

Maps and embeddings between hyperbolic spaces and their boundaries studied.

Proves existence and regularity of energy-minimizing maps between ideal hyperbolic simplicial complexes.

We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.

Unique geodesics selected by energy minimization in Teichmüller space.

Defines manifolds of mappings between function spaces and discusses their properties.

It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their Gromov boundaries. A more general question is to detect classes of functions between Gromov hyperbolic spaces that induce continuous maps between their Gromov boundaries. In this paper we introduce the cl…

Study shows most isometric submersions between Teichmüller spaces are forgetful.

Maps between classifying spaces for certain groups are studied, with rational cohomology results.

Paper investigates optimal transport map estimation in infinite-dimensional spaces.

The paper classifies holomorphic maps between Riemann surface configuration spaces.

This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the topological structure of the space of such maps. In particular, we show that the …

New map connects stability conditions to Teichmüller space.

We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being harmonic morphisms naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Wey…

In this paper, we give complete classifications of linear $\infty$-harmonic maps between Euclidean and Heisenberg spaces, between Nil and Sol spaces. We also classify all $\infty$-harmonic linear endomorphisms of Sol space and show that there is a subgroup of $\infty$-harmonic linear automorphisms in the group of linea…

Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has r…

Study numerical invariants under retraction maps between topological spaces.

New quantity helps map homotopy classes in complex spaces.

This paper shows similarities in deformation spaces of Kleinian groups and anti-holomorphic maps.

We study affine maps between CAT(0) spaces with geometric actions, and show that they essentially split as products of dilations and linear maps (on the Euclidean factor). This extends known results from the Riemannian case. Furthermore, we prove a splitting lemma for the Tits boundary of a CAT(0) space with geometric …

Study Lorentz harmonic maps and spacelike surfaces in anti-de Sitter space.

We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial structures is twistorial if and only if it is quaternionic. 2) A map between quaternion…

Study of conformal mappings in pseudo-Finsler spaces, extending results from pseudo-Riemannian geometry.

We study the space of "link maps": the space of maps of a disjoint union of compact, closed manifolds P_1, . . ., P_k into a manifold N whose images are pairwise disjoint. We apply the manifold calculus of functors developed by Goodwillie and Weiss to study the difference between it and its linear and quadratic approxi…

A map between twistor spaces is defined based on metrics, showing holomorphicity under specific conditions.

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also in…

Notes on quasiregular maps between Riemannian manifolds, preserving Sobolev forms.

New invariants found for mappings between non-symmetric affine spaces.

Local holomorphic maps preserving (p,p) forms are shown to be isometries.

Two constructions of classifying spaces for singular maps are connected.

Generalizes CNNs on homogeneous spaces like Euclidean and spherical surfaces.

Harmonic maps between symmetric spaces have duals.

We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.

We construct a tangential map from a locally symmetric space of noncompact type to its dual compact type twin. By comparing the induced map in cohomology to a map defined by Matsushima, we conclude that in the equal rank case the map has a nonzero degree.

Stability defined for maps between polarised varieties in higher dimensions.

Study spectral distances on compact RCD spaces.

Generalizes neural networks for infinite-dimensional mappings, including PDE solutions.

Mapping spaces of supermanifolds are usually thought as exclusively in functorial terms (i.e. trough the Grothendieck functor of points). In this work we provide a geometric description of such mapping spaces in terms of infinite-dimensional super-vector bundles.

Let $F : H^q \to H^q$ be a $C^k$-map between Sobolev spaces, either on $\mathbb R^d$ or on a compact manifold. We show that equivariance of $F$ under the diffeomorphism group allows to trade regularity of $F$ as a nonlinear map for regularity in the image space: for $0 \leq l \leq k$, the map $F: H^{q+l} \to H^{q+l}$ i…

In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.

Maps between acute triangles with minimal stretch found and studied.

Paper connects geometric intuition to algebraic structures.