arXiv research

Extends p-harmonic map theory for new properties.

The paper explores the twisted Rokhlin property in mapping class groups of surfaces.

Investigates maps and properties in spaces with negative dimensions and curvature.

Proves properties of sub-Riemannian exponential map, showing it's not injective.

Proves congruence subgroup property for mapping class groups of hyperbolic surfaces.

The paper extends a measure preserving property to bi-Lipschitz maps between Moran sets.

Abstracts a theorem for non-smooth maps in infinite dimensions.

Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalized distance-squared mapping of equidimensional case is not injective. Nevertheless, in this paper, it is shown that the non-singular property…

Paper proves energy identity and no-neck property for special harmonic maps.

Explains mapping properties of elliptic operators in conical spaces.

Harmonic map flow's singularity properties proven with Lojasiewicz inequalities.

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory a…

Study on finiteness properties of handlebody mapping class groups.

Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of smoothly local properties. In realising the definition of a local property at a pa…

Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.

Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.

We study generalized moment maps for a Hamiltonian action on a connected compact $H$-twisted generalized complex manifold introduced by Lin and Tolman and prove the convexity and connectedness properties of the generalized moment maps for a Hamiltonian torus action.

The study proves unique path lifting properties and their implications on quotient spaces and covering maps.

Introduces Hurewicz fibrations for embedding maps of orbifold charts.

Study on mapping class groups of infinite type surfaces.

Proves Congruence Subgroup Property for two types of groups.

Study shows conjugacy of torsion in genus 2 surfaces.

We prove that the mapping class group of a closed oriented surface of genus at least two does not have Kazhdan's property (T).

Study big mapping class groups and their co-Hopfian property, finding new examples and proving injective homomorphisms results.

The article studies mapping properties of Radon transform and backprojection on a unit ball.

Study maps in semidirect products of groups, proving Lipschitz properties without intrinsic dilations.

Investigates properties of moment maps and stratifications on Lie groups.

In this paper, we explore the fixed point theory of $n$-valued maps using configuration spaces and braid groups, focussing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane (resp.\ the $2$-sphere ${\mathbb S}^{2}$) has the Wecken property for …

Survey on random walks on mapping class groups and their properties.

Discussing rigidity properties of conics, inspired by billiards in ellipses.

New stretch maps minimize distortion in geometric group theory.

We study properties of shy maps in digital topology.

We provide a general framework to study convergence properties of families of maps. For manifolds $M$ and $N$ where $M$ is equipped with a volume form $\mathcal{V}$ we consider families of maps in the collection $\{(φ, B) : B \subset M, φ:B \rightarrow N\text{ with both measurable}\}$ and we define a distance function …

In this article, we prove a Liouville property of holomorphic maps from a complete Kahler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kahler manifold with a certain assumption on the sectional curvature.

The paper connects moment maps to the stability of holomorphic fibrations.

In [3] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for proper maps between orbifolds, which counts preimages of regular values with appropriate weights. We show that the mapping degree satisfies…

Introduces generalized moment maps for almost Hermitian settings.

We explore the intrinsic geometry of tangent bundles and properties of the mirror map.

Paper proves unique tangent maps for complex maps into algebraic varieties.

In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of metrics. We study geodesic mappings of Einstein spaces.

The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.

Study of pure mapping class groups on infinite graphs.

We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spa…

It is well-known that a paracompact space X is of covering dimension n if and only if any map f from X to a simplicial complex K can be pushed into its n-skeleton. We use the same idea to define dimension in the coarse category. It turns out the analog of maps f from X to K is related to asymptotically Lipschitz maps, …

Extends $p$-biharmonic and bi-$p$-harmonic map definitions.

The class of metrizable spaces $M$ with the following approximation property is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is $\e$-homotopic to $g$. It is shown that this class has very nice properties. For exam…

The paper studies global invertibility of maps on Finsler manifolds.

New proofs and refined theorems on bounded cohomology.