arXiv research

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 on the topology of leaves in singular Riemannian foliations.

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 …

Optimizes Lasso hyperparameters using leave-one-out CV.

New examples of non-homeomorphic foliation leaves found.

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

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

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

For a singular Riemannian foliation whose leaves are properly embedded, we show in the first part of this article the existence of global tubular neighbourhoods, and we develop a global description of the foliation as stratification by types of leaves. The second part deals with the further restriction to a foliation w…

We prove that for a generic $3$-dimensional integrable rolling distribution of contact elements (excluding developable seed and isotropic developable leaves) isometric correspondence of leaves of a general nature (independent of the shape of the seed) requires the Bäcklund transformation.

Extends foliation results to singular cases.

New examples of rigid Lie foliations with dense leaves found.

Compact foliations preserve entropy if leaves are strictly convex projective.

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…

Investigates metric degeneracies on symplectic leaves using a generalized gradient flow.

Holomorphic foliations found in ball space with unique properties.

Optimizes hyperparameter tuning for models using approximate leave-one-out cross-validation.

We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares intrinsic distances in leaves with extrinsic distances in the ambient space grows fast…

We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry). The result is also a generalization of Conn's linearization theorem from one-point leaves to arbitrary symplectic leaves (however, we do not make use of Conn's theorem).

We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not only extends but also provides a new approach (and proofs) to the classical stabili…

ALO-CV approximates leave-one-out error in proportional regime.

Paper accelerates conformal prediction by using approximate leave-one-out estimators.

For a connected abelian Lie group T acting on a Poisson manifold (Y,π) by Poisson isomorphisms, the T-leaves of π in Y are, by definition, the orbits of the symplectic leaves of π under T, and the leaf stabilizer of a T-leaf is the subspace of the Lie algebra of T that is everywhere tangent to all the symplectic leaves…

The paper explores symplectic foliations and their leaves on manifolds.

Non-exact Poisson structures found on toric varieties.

Let $F$ be a non-singular foliation on the plane with all leaves being closed subsets, $H^{+}(F)$ be the group of homeomorphisms of the plane which maps leaves onto leaves endowed with compact open topology, and $H^{+}_{0}(F)$ be the identity path component of $H^{+}(F)$. The quotient $π_0 H^{+}(F) = H^{+}(F)/H^{+}_{0}…

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…

Classifies neighborhoods around specific leaf structures.

The paper improves ALO for $\ell_1$-regularized models.

New proof of uniformization for hyperbolic foliations.

We prove that every closed, smooth $n$-manifold $X$ admits a Riemannian metric together with a smooth, transversely oriented CMC foliation if and only if its Euler characteristic is zero, where by CMC foliation we mean a codimension-one, transversely oriented foliation with leaves of constant mean curvature and where t…

We consider Lorentzian manifolds with parallel light-like vector field V. Being parallel and light-like, the orthogonal complement of V induces a codimension one foliation. Assuming compactness of the leaves and non-negative Ricci curvature on the leaves it is known that the first Betti number is bounded by the dimensi…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

The study finds dense orbits and absolute period leaves for complex flows.

UDM reparameterization improves language model generation.

In this paper, we study stability for harmonic foliations on locally conformal Kähler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact homogeneous spaces.

We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth instead of merely Gromov-Hausdorff. Corollaries include Reeb's local stability theor…

In this paper, we study a notion of hyperbolicity for hyperbolicity foliations with 1-dimensional parabolic leaves, namely the non-existence of holomorphic cylinders along the foliation - holomorphic maps from $\D^{n-1} \times \C$ to the manifold sending each $\{*\} \times \C$ to a leaf. We construct a tensor, that is …

Study foliations on Riemannian manifolds with specific vector fields, focusing on geometric properties.

Let $X$ be an $(n+1)$-dimensional manifold, $Δ$ be a one-dimensional foliation on $X$, and $p: X \to X / Δ$ be a quotient map. We will say that a leaf $ω$ of $Δ$ is special whenever the space of leaves $X / Δ$ is not Hausdorff at $ω$. We present necessary and sufficient conditions for the map $p: X \to X / Δ$ to be a l…

Let (M, F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we say that (M, F) has the Liouville property. Our main result is that codimension-on…

The study classifies natural almost Hermitian structures on specific Lie groups.

The paper proves new comparison theorems for sub-Laplacian in foliations with minimal leaves.

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of arbitrary codimension if there exists a closed p form which evaluates positively on e…

Study shows how to deform foliated manifolds with flat leaves, leading to geometric characterization.

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

Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.

Let $f:M\to M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded in $M$.