arXiv research

Characterizes surfaces made from strips with boundary leaves.

The paper proves a foliation of a manifold with specific properties.

The paper establishes a correspondence between normal distributions and neat foliations on manifolds with boundary.

Let f:M->M be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of f. This is proved by thorough study of the accessible boundaries of the center-stable and the center…

A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the image of the boundary does.

The paper studies homeotopy groups of leaf spaces for specific foliations.

Thurston's boundary to the universal Teichmüller space $T(\mathbb{D})$ is the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of $\mathbb{D}$. A geodesic ray in $T(\mathbb{D})$ is of Teichmüller type if it shrinks vertical foliation of an integrable holomorphic quadratic differential. In a prio…

The paper explores symplectic foliations and their leaves on manifolds.

The paper proves bounds on mean curvature for CMC foliations with Ricci curvature constraints.

For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of $L^2$ harmonic forms of fixed degree with the images of maps between intersection cohomology groups of an associated stratified space obtained by collapsing the fibres of the fibration at infinity onto its base. In the pr…

New mathematical surfaces without boundaries found.

The paper studies the homeotopy groups of foliations on surfaces.

The paper addresses boundary term learning in reflected diffusion models.

The paper studies diffeomorphisms of a specific foliation on a Klein bottle.

Study finds optimal boundaries for hedging a perpetual American put option.

Study of diffeomorphisms groups on lens spaces with Morse-Bott foliations.

Given a general pseudo-Anosov flow in a three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We compactify this orbit space with an ideal circle boundary. If there are no perfect fits between stable and unstable leaves and the flow is not topologically conjugate to …

Solves inverse problem for Calderón using microlocal normal forms.

We extend the techniques of [CH] to build an inductive procedure for studying actions in the boundary of the Culler-Vogtmann Outer Space, the main novelty being an adaptation of he classical Rauzy-Veech induction for studying actions of surface type. As an application, we prove that a tree in the boundary of Outer spac…

Contractible diffeomorphism groups on lens spaces derived from Morse-Bott foliations.

Let X be a smooth compact manifold with boundary. For smooth foliations on the boundary of X admitting a `resolution' in terms of a fibration, we construct a pseudodifferential calculus generalizing the fibred cusp calculus of Mazzeo and Melrose. In particular, we introduce certain symbols leading to a simple descripti…

A taut foliation of a hyperbolic 3-manifold has the continuous extension property for leaves in almost every direction; that is, for each leaf of the universal cover of the foliation and almost every geodesic ray in the leaf, the limit of the ray in the universal cover of the 3-manifold is a well-defined point in the i…

Study automorphism groups of Reeb components with complex leaves and solve functional equations.

Study index theory for foliated manifolds with boundary using blup groupoids.

An alternate proof shows how foliation extensions work in 3D spaces.

Study non-compact surfaces formed by gluing strips and their foliations.

We study codimension one foliations with singularities defined locally by Bott-Morse functions on closed oriented manifolds. We carry to this setting the classical concepts of holonomy of invariant sets and stability, and prove a stability theorem in the spirit of the local stability theorem of Reeb. This yields, among…

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves of the latter are classified by restrictions of the bundles to certain divisors.…

The study characterizes lamination limits and homeomorphisms in 3D handlebodies.

Let $X_0$ be a compact Riemannian manifold with boundary endowed with a oriented, measured even dimensional foliation with purely transverse boundary. Let $X$ be the manifold with cylinder attached and extended foliation. We prove that the $L^2$--measured index of a Dirac type operator is well defined and the following…

In-plane drill rotations are impossible for smooth shells.

A trace formula for foliated flows on closed manifolds.

A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this kind of invariants, which means that the definition is satisfied with the same con…

Study examines influence diagnostics in high-dimensional M-estimation.

Study on the topology of leaves in singular Riemannian foliations.

We address the problem of existence and uniqueness of a Levi-flat hypersurface $M$ in $C^n$ with prescribed compact boundary $S$ for $n\ge3$. The situation for $n\ge3$ differs sharply from the well studied case $n=2$. We first establish necessary conditions on $S$ at both complex and CR points, needed for the existence…

The paper explores holographic structures on exotic spheres and their implications.

We investigate the coarse homology of leaves in foliations of compact manifolds. This is motivated by the observation that the non-leaves constructed by Schweitzer and by Zeghib all have non-finitely generated coarse homology. This led us to ask whether the coarse homology of leaves in a compact manifold always has to …

Study automorphisms of complex foliations in 3D.

Let M be a compact surface of negative Euler characteristic and let C(M) be the deformation space of convex real projective structures on M. For every choice of pants decomposition for M, there is a well known parameterization of C(M) known as the Goldman parameterization. In this paper, we study how some geometric pro…

Optimizes Lasso hyperparameters using leave-one-out CV.

Infinite fractal tree solves shortest connection problem.

New examples of non-homeomorphic foliation leaves found.

Proves isometric correspondence of leaves for generic rolling distributions.

Study shows conditions for continuity of foliated homeomorphisms action on space of leaves.

Lie foliations with symmetric leaves are smoothly conjugate to homogeneous ones.

The paper studies T-leaves and stabilizers in Poisson structures on flag varieties.

Defines foliation criterion for dense isoperiodic leaves in rank 1 affine orbifolds.