arXiv research

Geodesic mappings found in a specific type of warped product manifolds.

Deform moment map on symplectic connections using star product algebras.

Harmonic maps from hyperbolic planes to hyperbolic space exist with given boundary data.

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

Quasi-isometries in horospherical products are close to product maps.

We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked poin…

Constructs correspondences on hyperelliptic surfaces combining orbifold groups and Blaschke products.

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…

We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to …

Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.

Sobolev maps on product spaces are split or approximately split.

Study of symmetries in deformed q-map spaces reveals a complex group structure.

Study on embedding tree products into groups, distinguishing them.

Author defines products of elements in cobordism-like modules induced from generic maps.

Two constructions of classifying spaces for singular maps are connected.

In this paper we introduce various associative products on the homology of the space of knots and singular knots in $S^n$. We prove that these products are related through a desingularization map. We also compute some of these products and prove the nontriviality of the desingularization morphism.

Affine maps reveal higher rank structures in certain spaces.

Currents on Lie groups form a Hopf algebra structure.

The paper explores geometric properties of Riemannian warped product maps and their curvature.

Paper defines and studies Clairaut warped product Riemannian maps.

We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non-zero degree from products of closed manifolds of positive dimension. Particular examples include all manifolds of non-positive sectional curvature of rank one and all irreducible locally symmetric spaces of …

Real blow-up, including inhomogeneous versions, of boundary faces of a manifold (with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be particular cases of `generalized boundary blow-up' in which a new manifold and blow-down…

In this paper we develop the metric theory for the outer space of a free product of groups. This generalizes the theory of the outer space of a free group, and includes its relative versions. The outer space of a free product is made of $G$-trees with possibly non-trivial vertex stabilisers. The strategies are the same…

We prove minimal entropy rigidity for complete, finite volume manifolds locally isometric to a product of rank one symmetric spaces of dimension at least 3: the locally symmetric metric uniquely minimizes (normalized) entropy among all Riemannian metrics. The corresponding theorem is true for maps into these spaces as …

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 …

In this paper, we establish the rigidity result for local holomorphic volume preserving maps from an irreducible Hermitian manifold of compact type into its Cartesian products.

The paper characterizes biharmonic submersions from product manifolds.

We study obstructions to the existence of closed Fedosov's star products on a given Kähler manifold. In our previous paper, we proved that the Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of Connes-Flato-Sternheimer) Fedosov's star product only if it is a zero of the Cahen-Gutt moment…

For a Poincare duality space X and a map X -> B, consider the homotopy fiber product X x^B X. If X is orientable with respect to a multiplicative cohomology theory E, then, after suitably regrading, it is shown that the E-homology of X x^B X has the structure of a graded associative algebra. When X -> B is the diagonal…

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to characterize holomorphic maps $φ:{\Bbb C}^{m}\supset U\longrightarrow {\Bbb C}^{n}…

Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.

Flexible surfaces found in complex projective and product spaces.

The author connects Poincaré embeddings to Reidemeister traces and diagonal maps.

Thurston obtained a classification of individual surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichmüller space. In this paper we present certain extended versions of this, first, to random products of homeomorphisms and second, to holomorphic self-maps of Teichmüller spaces.

Study monodromy relations in Seifert fibered spaces for 3-manifold fillings.

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book by Baird and Wood for details)…

The Landau-Lifshitz equation is derived as the reduction of a geodesic flow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced space is an example of semidirect product reduction by stages.

We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on $\text{Out}(F_N)$, each time under a finite second moment condition on the measure (either with respect to the Teichmüller metric, or with respect to the Lipschitz metric …

We prove the equivalence between a relative bottleneck property and being quasi-isometric to a tree-graded space. As a consequence, we deduce that the quasi-trees of spaces defined axiomatically by Bestvina-Bromberg-Fujiwara are quasi-isometric to tree-graded spaces. Using this we prove that mapping class groups quasi-…

Unique median structures found in hyperbolic spaces.

Defines a bundle map for currents on manifolds using higher covariant derivatives.

Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circe). We explain the geometric meaning of this series as degrees of maps of some grand configurat…

The paper studies conditions for Cannon-Thurston maps in trees of hyperbolic spaces.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds $B$ and $F$ into the doubly warped product $_{f}B\times_{b}F$ can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections $_{f}B\times_{b}…

Graph products inherit Morse local-to-global property from their components.

Geometric cohomology model uses co-oriented maps to define a product structure.

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, rank 1 CAT(0) groups, mapping class groups and Out(Fn). As an application, we show that mapping clas…