Simple foliated flowsmath.GT
Simple flows on manifold foliations.
problem Transversely oriented foliations on closed manifolds.
method Simple foliated flows on codimension one.
result Existence of simple foliated flows on manifolds.
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48 results for “foliation flows”
Paper introduces entropy for Riemannian foliations and connects it to Ricci flow.
problem Entropy functional for Riemannian foliations and its relation to Ricci flow.
method Introduced entropy functional and related its gradient flow to transverse Ricci flow.
result Entropy functional is monotonic along transverse Ricci flow and related to it.
Defines and calculates foliation homology from flows.
problem Homology of foliations defined by flows.
method Definition and calculation of foliation homology.
result Homology naturally associated with Seifert fibration.
Paper proves S-stability of foliations on flow-spines with transverse Reeb flow.
problem Characterizing S-stable foliations on flow-spines with transverse Reeb flow.
method Introduced S-stability for foliations on branched simple polyhedrons and proved stability for 1-forms with .
result Proved the number of simple tangency points of an S-stable foliation on a flow-spine is at least 2.
The paper solves a 5-manifold foliation problem using a Sasaki-Ricci flow.
problem Solving foliation singularities on Sasakian 5-manifolds.
method Applying the Sasaki-Ricci flow to resolve cyclic quotient foliation singularities.
result Proves a Sasaki analogue of the analytic minimal model program.
Extends symplectic flow results to foliations.
problem Applying hard Lefschetz theorem to symplectic foliations.
method Generalizes results from symplectic flows to foliations.
result Extends transversal hard Lefschetz theorem to transversely symplectic foliations.
Study of foliations on symmetric spaces and mean curvature flow results.
problem Understanding foliations on symmetric spaces with non-negative curvature.
method Proving foliations are isoparametric and applying mean curvature flow.
result Ancient solutions to mean curvature flow of regular leaves.
Study on minimal foliations in 3D manifolds with specific conditions.
problem Characterizing minimal foliations in 3D manifolds.
method Analyzing Anosov foliations and their intersections.
result Necessary and sufficient conditions for orbit foliation of Anosov flows.
Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spacesmath.DG
In this paper, we investigate the mean curvature flows starting from all non-minimal leaves of the isoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation exists in infin…
This paper constructs hyperbolic 3-metrics using Ricci flow foliation.
problem Creating asymptotically hyperbolic 3-metrics.
method Using Ricci flow foliation on 3-manifolds.
result Established asymptotically hyperbolic 3-metrics with Ricci flow foliation.
A foliation is R-covered if the leaf space in the universal cover is homeomorphic to the real numbers. We show that, up to topological conjugacy, there are at most two pseudo-Anosov flows transverse to such a foliation. If there are two, then the foliation is weakly conjugate to the the stable foliation of an R-covered…
Foliation Theorymath.GT
Enhances foliation results for non- codimension one foliations.
problem Classical foliation results for non- foliations.
method Flow box decompositions and enhancements of classical results.
result Extensions of foliation results to non- foliations.
The paper studies Liouville structures for taut foliations and Anosov flows, proving their topological invariance.
problem Understanding the topological invariance of Liouville structures for taut foliations and Anosov flows.
method Combining smoothing schemes for topological conjugacies and a refinement of Vogel's uniqueness result.
result Liouville structures are topological invariants of taut foliations and orbit equivalent Anosov flows.
Extends Masur's divergence theorem to complex tori and Kummer surfaces.
problem Establishing uniquely ergodic horizontal foliations for geodesic flows on moduli spaces.
method Defined and calculated horizontal foliations and geodesic flows on moduli spaces of Kähler metrics.
result Proved that horizontal foliations are uniquely ergodic if geodesic flows are recurrent.
We prove a general result about the short time existence and uniqueness of second order geometric flows transverse to a Riemannian foliation on a compact manifold. Our result includes some flows already existing in literature, as the transverse Ricci flow, the Sasaki-Ricci flow and the Sasaki J-flow and motivates the s…
We prove the existence of foliations transverse to pseudo-Anosov flows using veering triangulations.
problem Existence of foliations transverse to pseudo-Anosov flows in 3-manifolds.
method Combinatorial approach via veering triangulations and branched surfaces.
result Existence of transverse foliations for certain pseudo-Anosov flows.
Study on transverse Ricci solitons on compact foliated manifolds.
problem Characterizing transverse Ricci solitons on compact foliated manifolds.
method Investigation of self-similar solutions of the transverse Ricci flow, analysis of taut Riemannian foliations.
result Established relations between taut Riemannian foliations and transverse Ricci solitons, found examples of transverse Ricci solitons.
Paper constructs flows converging to cones and foliations.
problem Understanding mean curvature flow convergence to cones and foliations.
method Constructs a family of mean curvature flows converging to cones and foliations under specific conditions.
result Flow converges to area minimizing, strictly stable hypercone and Hardt-Simon foliation of the cone.
The paper explores universal circles for Anosov foliations and their uniqueness.
problem Exploring the uniqueness of universal circles for Anosov foliations.
method Using the flow space of an Anosov flow to parameterize the circle bundle at infinity of the foliations.
result Several constructions of a universal circle are typically distinct and not conjugate.
The paper proves Harnack inequalities on foliations with Ricci flow.
problem Proving Harnack inequalities on foliations with Ricci flow.
method Using transverse Ricci flow on totally geodesic Riemannian foliations, the paper proves two types of differential Harnack inequalities and a time-dependent curvature dimension inequality.
result The paper establishes Harnack inequalities and heat kernel upper bounds.
Study of centralizer elements preserving geodesic flow foliations on covers.
problem Rigidity properties of centralizer elements in geodesic flows.
method Definition and study of foliated centralizer, proving rigidity properties.
result Foliated centralizer is a finite-dimensional Lie group, discrete unless metric is homothetic to real hyperbolic.
The paper introduces new metric structures on -foliations and uses a flow to deform them.
problem Developing new flexible metric structures on -foliations.
method Introducing new metric structures and using the partial Ricci flow to deform them.
result Deformation retraction of new structures with positive partial Ricci curvature onto classical structures.
Reeb flow made transverse to foliations without invariant measures.
problem Making Reeb flow transverse to foliations without invariant measures.
method Leafwise Brownian motion to construct transverse measures.
result Reeb flow has no contractible orbits when transverse to foliations without invariant measures.
The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.
Surveying isoparametric foliations and related geometric constructions.
problem Constructing isoparametric foliations using Clifford algebra.
method Representation theory of Clifford algebra and mean curvature flow.
result Investigation of geometric constructions related to isoparametric hypersurfaces.
Study shows how to compute manifold's characteristic numbers from flow properties.
problem Computing characteristic numbers of manifolds.
method Analyzes singular Riemannian flows and their foliations.
result Characteristic numbers computed as residues of infinitesimal foliations.
Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend continuously to the sphere at infinity, hence the limit sets are continuous images of…
Constructs foliations of lightcones using surfaces of constant spacetime mean curvature.
problem Creating foliations of lightcones with specific geometric properties.
method Employing a geometric flow inspired by Huisken-Yau's approach for Riemannian settings.
result Initial data converges exponentially to an STCMC surface under area preserving null mean curvature flow.
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and estimate the existence time of solutions for some particular cases. The key step of t…
Extrinsic Geometric Flow (EGF) for a codimension-one foliation has been recently introduced by authors as deformations of Riemannian metrics subject to quantities expressed in terms of its second fundamental form. In the paper we introduce soliton solutions to EGF and study their geometry for totally umbilical foliatio…
Anosov flows' orbit complements are hyperbolic manifolds.
problem Characterizing hyperbolicity of Anosov flow orbit complements.
method Analyzing foliations and periodic orbits in 3D manifolds.
result Complement of any filling periodic orbit in Anosov flows is hyperbolic.
New proof shows left orderability of 3-manifold groups with specific foliations.
problem Left orderability of 3-manifold groups with co-orientable taut foliations.
method Analyzes co-orientable taut foliations with orderable cataclysm to prove left orderability of 3-manifold fundamental groups.
result Proves left orderability of 3-manifold groups with specific foliations.
Study on MCF of foliations, focusing on singular cases.
problem Investigate mean curvature flow of foliations with singularities.
method Generalizes previous results on MCF of foliations, focusing on singular cases.
result Finite time singularities are singular leaves of type I under bounded curvature conditions.
Characterizes flag geometries for Hitchin representations in SL3(R).
problem Understanding flag geometries associated with Hitchin representations in SL3(R).
method Geometric characterization based on invariant foliations and refraction flows.
result Constructs refraction flows for positive roots in general sl_n(R), with highest root flows being C^1+α.
We study the transversal wave equation on a compact Riemannian foliated manifold. As applications, we get an Egorov's type theorem for transversally elliptic operators, state a relationship between the singularities of the Fourier transform of the spectrum distribution function of a transversally elliptic operator and …
A flow of metrics, , on a manifold is a solution of a differential equation $\dt g = S(g)$, where a geometric functional is a symmetric -tensor usually related to some kind of curvature. The mixed sectional curvature of a foliated manifold regulates the deviation of leaves along the leaf geodesics. W…
Study shows how certain foliations in unit tangent bundles behave.
problem Characterizing behavior of foliations in unit tangent bundles.
method Analyzing intersections and properties of foliations.
result Certain partially hyperbolic diffeomorphisms are collapsed Anosov flows.
We study the behavior of the Yang-Mills flow for unitary connections on compact and non-compact oriented surfaces with varying metrics. The flow can be used to define a one dimensional foliation on the space of SU(2) representations of a once punctured surface. This foliation universalizes over Teichmüller space and is…
The paper confirms a conjecture about foliating almost Fuchsian manifolds with CMC surfaces.
problem Confirming a conjecture about foliating almost Fuchsian manifolds with CMC surfaces.
method Proving the long-time existence and convergence of a modified mean curvature flow.
result The CMC foliation conjecture is confirmed for a subclass of almost Fuchsian manifolds.
Researchers compute de Rham cohomology of geodesic flow foliations on hyperbolic surfaces.
problem Answering a problem posed by Haefliger and Li about geodesic flow foliations.
method Unitary representation theory of PSL(2, R) and Hodge decompositions of de Rham complexes.
result Computed de Rham cohomology of weak stable foliations for various coefficients.
We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation. Then the Extrinsic Geometric Flow depending on the second fundamental form of the…
Study shows universal circle isomorphic to flow space ideal boundary.
problem Understanding foliations and pseudo-Anosov flows in 3-manifolds.
method Analyzing depth-one foliations and pseudo-Anosov flows in atoroidal 3-manifolds.
result Universal circle is isomorphic to flow space ideal boundary.
We prove here that given a proper isometric action on a complete Riemannian manifold then every continuous isometric flow on the orbit space is smooth, i.e., it is the projection of an -equivariant smooth flow on the manifold . As a direct corollary we infer the smoothness of isometric …
New 3D shapes found without certain flows.
problem Finding 3D shapes without specific flows.
method Using foliations and pseudo-Anosov flows, analyzing cusped hyperbolic 3-manifolds.
result First examples of 3D shapes without veering triangulations.
The paper studies foliation flows with logarithmic speeds and finds convergence to translating solutions.
problem Flowing foliations with specific curvature speeds and analyzing convergence behavior.
method Analyzes foliations of with speeds , focusing on uniformly convex hypersurfaces.
result There is a distinct leaf such that flows starting from it converge to a translating solution.
Study mean curvature flow in hyperbolic 3-manifolds, proving foliations and existence of minimal surfaces.
problem Existence and properties of foliations in hyperbolic 3-manifolds.
method Mean curvature flow, surgery, min-max theory, foliations, continuity of minimal surfaces.
result Existence of smooth entire foliations in quasi-Fuchsian and hyperbolic 3-manifolds.
Example shows unique ergodicity of foliations on surfaces.
problem Unique ergodicity of foliations on surfaces.
method Construction of example and geometric criterion.
result Horizontal foliation is uniquely ergodic under certain conditions.
Anosov flow found in specific partially hyperbolic systems.
problem Characterizing partially hyperbolic diffeomorphisms with center foliation.
method Analyzing transitive dynamically coherent systems with one-dimensional center foliation.
result Discretized Anosov flow found in systems satisfying for center leaves.