arXiv research

Study on harmonic maps on weighted Riemannian foliations.

Defines basic Albanese maps for foliated Riemannian manifolds.

The paper studies critical points of horizontal energy functional in Riemannian foliations.

Study foliations from complex ball to another via harmonic maps.

Develops twistor theory for foliated manifolds, proving orbifold results.

Proves geometric invariance of signature and cohomology for Riemannian foliations.

Paper finds lower bounds for foliation maps under spin condition.

Proves generalized Chen's conjecture for biharmonic maps on foliations.

Examines how meridians and parallels help in map drawing.

Quadratic-time algorithm computes stretch factors and foliations for pseudo-Anosov mapping classes.

Taut foliations map leaves to branched 2-sphere covers.

A singular foliation on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This …

We study the transversally harmonic maps between foliated Riemannian manifolds. In particular, we prove that under some curvature conditions, any transversally harmonic map is transversally totally geodesic.

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

Anosov maps study with new Banach space and foliation method.

Study the pullbacks and blowups of Lie algebroids and related structures.

The paper proves a Liouville theorem for a specific type of harmonic maps on foliated manifolds.

New maps connect universal circles to ideal sphere for hyperbolic manifolds.

The author studies regions foliated by 1D families of functions and their applications.

Proves an index theorem for foliations using spectral triples.

Study examines conditions for quotient maps of foliated manifolds to be locally trivial.

The volume of a k-dimensional foliation $\mathcal{F}$ in a Riemannian manifold $M^{n}$ is defined as the mass of image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing a construction by Gluck and Ziller, "singular" foliations by 3-spheres are constructed on…

Abstract shows mapping between foliation characteristic classes.

The paper studies critical maps of a specific energy functional on pseudo-Hermitian manifolds.

Study on Clairaut maps from nearly Kahler to Riemannian manifolds.

In this paper we study singular riemannian foliations that have sections,i.e., totally geodesic complete immersed submanifolds that meet each leaf orthogonally and whose dimensions are the codimensions of the regular leaves. We prove here that the restriction of the foliation to a slice of a leaf is diffeomorphic to an…

Develops Chern-Weil theory for singular foliations.

The study describes how quadratic differentials influence foliations on Riemann surfaces.

The paper generalizes a theorem and introduces a new characteristic map for foliated manifolds.

Sharp spectral estimates for negatively curved foliations.

Consider a singular Riemannian foliation (s.r.f for short) on a compact manifold. By successive blow-ups along the strata, we construct a regular Riemannian foliation on another compact Riemannian manifold and a desingularization map that projects leaves of the regular Riemannian foliation into leaves of the s.r.f. Thi…

New Teichmüller geodesic rays found with unique foliations.

The paper proves left-orderability for certain Dehn fillings of pseudo-Anosov mapping tori.

Maps on foliated manifolds decrease area and scalar curvature is negative.

We introduce the concept of morphism of pseudogroups generalizing the étalé morphisms of Haefliger. With our definition, any continuous foliated map induces a morphism between the corresponding holonomy pseudogroups. The main theorem states that any morphism between complete Riemannian pseudogroups is complete, has a c…

The paper proves isomorphisms between two complexes related to singular foliations.

We show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps the Reeb class of the symplectic foliation to the modular class of the Poisson manifold. The Riemannian interpretation of those classes wil…

Using the method of Witten deformation, we express the basic index of a transversal Dirac operator over a Riemannian foliation as the sum of integers associated to the critical leaf closures of a given foliated bundle map.

Paper generalizes Schwarz lemma for harmonic maps between Riemannian manifolds.

A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is called a polar foliation if, for each regular point $p$, there is an immersed submanifold $Σ$, called section, that passes through $p$ and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the part…

The paper proves properties of Finsler submanifolds and analytic maps.

Study of Matsumoto maps on foliated bundles over hyperbolic manifolds.

Study on mapping class groups of non-orientable surfaces, proving some conjectures and refuting others.

This paper simplifies complex nonholonomic systems using momentum map reduction.

This paper has three parts. The first part is a general introduction to rigidity and to rigid actions of mapping class group actions on various spaces. In the second part, we describe in detail four rigidity results that concern actions of mapping class groups on spaces of foliations and of laminations, namely, Thursto…

Paper translates train track concepts to cluster algebras for pseudo-Anosov mapping classes.

Study defines a new invariant for foliated manifolds, linking index of Dirac operator to cohomology.

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, whi…