Horizontal surgery on pseudo-Anosov flows yields almost equivalent flows.
problem Understanding and manipulating pseudo-Anosov flows.
method Performing horizontal surgery on pseudo-Anosov flows by cutting along specific annuli and regluing with a Dehn twist.
result Horizontal Goodman surgery on transitive pseudo-Anosov flows yields an almost equivalent flow.
Smooth orbit equivalence proves metric equivalence for geodesic flows.
problem Proving metric equivalence for geodesic flows under orbit equivalence.
method Proving metric equivalence for geodesic flows under orbit equivalence.
result Smooth orbit equivalence implies conformal equivalence of metrics.
Odd covers have one Anosov flow, even covers have two.
problem Classifying Anosov flows on 3-manifolds with specific covers.
method Analyzing finite covers of geodesic flows on 3-manifolds.
result Odd covers result in one Anosov flow class, even covers in two.
Paper proves equivalence of two Floer theories using pearly trees and Hamiltonian flows.
problem Proving equivalence between two Floer theories.
method Using pearly tree discs and local Hamiltonian flows.
result Equivalence relation between immersed Lagrangian Floer theory and Hamiltonian immersed Lagrangian Floer theory.
Generalizes Anosov flows to partially hyperbolic diffeomorphisms.
problem Classifying partially hyperbolic diffeomorphisms.
method Introducing collapsed Anosov flows and self orbit equivalences.
result All examples in Bonatti et al. belong to the collapsed Anosov flow class.
New method shows pseudo-Anosov flows on graph manifolds can be simplified.
problem Understanding pseudo-Anosov flows on graph manifolds.
method Constructing a partial Birkhoff section with genus one components that misses finitely many closed orbits.
result Every pseudo-Anosov flow on a graph manifold is almost equivalent to a totally periodic flow or a suspension Anosov flow.
New insights into pseudo-Anosov flows with special periodic orbits.
problem Understanding pseudo-Anosov flows with periodic orbits in 3-manifolds.
method Analyzing the topological features corresponding to trees of scalloped regions and classifying flows with the same free homotopy data.
result Explicit examples of flows with the same free homotopy data but not orbit equivalent.
The paper proves rigidity results for Anosov flows and their orbit equivalences.
problem Characterizing orbit equivalences of Anosov flows and their dynamics.
method Using hyperbolic-like dynamics, the paper proves a spectral rigidity theorem and gives efficient criteria for orbit equivalences.
result Characterizes orbit equivalent flows in terms of fundamental group elements represented by periodic orbits.
Geodesic flows on Kähler manifolds are quantum integrable when metrics are c-projectively equivalent.
problem Quantum integrability of geodesic flows on Kähler manifolds under c-projective equivalence.
method Construction of Poisson-commuting integrals of motion and their quantum counterparts.
result The geodesic flow's integrals of motion commute as quantum operators, leading to separation of variables in Schrödinger's equation.
We show that a self orbit equivalence of a transitive Anosov flow on a 3-manifold which is homotopic to identity has to either preserve every orbit or the Anosov flow is R-covered and the orbit equivalence has to be of a specific type. This result shows that one can remove a relatively unnatural assumption…
Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.
Algorithm decides if pseudo-Anosov flows have perfect fits.
problem Determining if pseudo-Anosov flows have specific asymptotic properties.
method Algorithm based on box decompositions and universal cover analysis.
result Algorithmic decision on pseudo-Anosov flows' perfect fit status.
The study finds infinitely many periodic orbits that can be used to modify Anosov flows.
problem Can surgeries on periodic orbits of Anosov flows produce equivalent flows?
method Analyzing suspension Anosov flows, the study identifies pairs of periodic orbits that can be used to modify the flow.
result For some suspension Anosov flows, there exist infinitely many pairs of periodic orbits that can be used to modify the flow.
Ancient curve shortening flows have entropy and curvature bounds equivalent.
problem Bounding entropy and total curvature for ancient curve shortening flows.
method Equivalence of entropy and total curvature conditions for ancient curve shortening flows.
result Entropy and total curvature bounds are equivalent for ancient curve shortening flows.
Classifies pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
problem Classifying pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
method Generalized Anosov-like actions on bifoliated planes, ideal boundary analysis.
result Pseudo-Anosov flows on 3-manifolds are determined up to orbit equivalence by their ideal boundary actions.
Characterizes Anosov flows via contact geometry.
problem Understanding Anosov 3-flows through contact geometry.
method Investigates interactions with Reeb dynamics and proves a technical theorem.
result Space of adapted geometries homotopy equivalent to Anosov flows.
Constructs graph manifolds with many Anosov flows.
problem Finding graph manifolds supporting multiple Anosov flows.
method Cutting geodesic flows, pulling back to finite covers, and gluing compatible pairs of flows.
result Constructs graph manifolds with at least n Anosov flows for any n.
New abelian cohomology theory applied to rigidity of flows.
problem Rigidity of Anosov flows and negatively curved surfaces.
method Development of abelian Livshits theory for transitive Anosov flows.
result Abelian Livshits theorem for homologically full Anosov flows.
In this paper, we first develope the concept of Lyapunov graph to weighted Lyapunov graph (abbreviated as WLG) for nonsingular Morse-Smale flows (abbreviated as NMS flows) on S3. WLG is quite sensitive to NMS flows on S3. For instance, WLG detect the indexed links of NMS flows. Then we use WLG and some other tool…
Extends Hard Lefschetz Property to isometric flows and shows equivalence.
problem Studying the Hard Lefschetz Property in isometric flows.
method Extending the Hard Lefschetz Property to isometric flows and proving equivalence.
result Equivalence of transverse and non-transverse Hard Lefschetz Properties in isometric flows.
We provide a written proof of a result due to H. Minakawa, which states that all suspension Anosov flows generated by hyperbolic matrices with positive trace are pairwise almost equivalent. The proof relies on constructing, for any given suspension flow, a genus-one Birkhoff section whose first-return map has fewer fix…
Study of flows on 7D manifolds with holomorphic properties.
problem Characterizing transversely holomorphic partially hyperbolic flows.
method Analyzing flows with biholomorphic holonomy pseudo-group, proving properties under integrable subcenter distribution.
result Flow projects to a transversely holomorphic Anosov flow on a 5D manifold.
Study shows equivariant Khovanov homotopy types are equivalent.
problem Understanding equivariant structures in Khovanov homotopy types.
method Investigates group actions on homotopy coherent diagrams to prove equivalence.
result Equivariant Khovanov homotopy types are equivariantly stably homotopy equivalent.
New perspective on Ricci flow on spheres using Minkowski spacetime.
problem Classifying singularity models for null mean curvature flow in Minkowski spacetime.
method Equivalence of 2d-Ricci flow and null mean curvature flow on lightcones.
result Classification of singularity models for null mean curvature flow.
It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the n-wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on …
New surgery method preserves Anosov flow properties using bi-contact geometry.
problem Defining a new type of surgery on Anosov flows.
method Bi-contact geometry and Reeb dynamics.
result Necessary and sufficient condition for generating contact Anosov flows.
Study homotopy equivalence of spaces of gradient-like flows and Morse functions on surfaces.
problem Understanding the topology of spaces of smooth functions and flows on surfaces.
method Proves homotopy equivalence of spaces of gradient-like flows and Morse functions on surfaces, with detailed decomposition into orbits.
result Spaces of gradient-like flows and Morse functions on surfaces are homotopy equivalent to manifolds.
This paper shows equivalence between SVGD and BBVI using kernel gradient flows.
problem Bayesian inference methods and their equivalence.
method Formalizes equivalence between SVGD and BBVI using kernel gradient flows.
result BBVI corresponds precisely to SVGD when using the neural tangent kernel.
Study describes global existence and convergence of flows on surfaces and fibrations.
problem Global existence and convergence of flows on surfaces and fibrations.
method Complete description of Ricci-Yang-Mills flow and pluriclosed flow on Tk bundles over Riemann surfaces. result Equivalence of solutions to generalized Ricci flow and pluriclosed flow with symmetry.
New measure defined for Brakke flow, linking classical and new definitions.
problem Defining and characterizing the Brakke flow.
method Introduced a space-time-Grassmann measure to characterize the flow.
result Equivalence between classical and new definitions of the Brakke flow.
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.
In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show …
Modeling bone microarchitecture adaptation using geometric flows.
problem Bone microarchitecture adaptation modeling.
method Advection and mean curvature flow model with a sphere as a test case.
result Closed-form solution for sphere under advection and mean curvature flow.
Study of flows on complex manifolds with holomorphic properties.
problem Global rigidity of transversely holomorphic Anosov flows on smooth compact manifolds.
method Analyzing the integrability of unstable and stable distributions, proving uniqueness in low dimensions.
result For topologically transitive flows, they are either orbit equivalent to a hyperbolic automorphism or geodesic flow.
We investigate the Kähler-Ricci flow modified by a holomorphic vector field. We find equivalent analytic criteria for the convergence of the flow to a Kähler-Ricci soliton. In addition, we relate the asymptotic behavior of the scalar curvature along the flow to the lower boundedness of the modified Mabuchi energy.
Constructs Anosov flows in hyperbolic 3-manifolds, disproving a conjecture.
problem Proving existence of infinitely many distinct Anosov flows in certain 4-manifolds.
method Using Cannon-Thurston maps and pseudo-Anosov quasigeodesic flows.
result Infinitely many distinct Anosov flows in some 4-manifolds.
We first prove rigidity results for pseudo-Anosov flows in prototypes of toroidal 3-manifolds: we show that a pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically equivalent to a geodesic flow and we show that a pseudo-Anosov flow in a solv manifold is topologically equivalent to a susp…
Let Φ be a flow on a smooth, compact, finite-dimensional manifold M. Consider the subsets E(Φ) and D(Φ) of C∞(M,M) consisting of smoothh mappings and diffeomorphisms (respectively) of M preserving the foliation of the flow Φ. Let also E0(Φ) and D0(Φ) be the identity path components of $E…
For some class of geometric flows, we obtain the (logarithmic) Sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non-collapsing and non-inflated properties, which generalize the results in the case of Ricci flow or List-Ricci flow or harmonic-Ricci flow. As applic…
Proposes a Carbon Equivalence Principle for financial products to align incentives and drive sustainability.
problem Align financial market incentives with carbon emissions to limit global warming.
method Introduces a Carbon Equivalence Principle requiring financial products to describe equivalent carbon flows alongside cash flows.
result Transparency of carbon flows in financial products can align incentives and reduce future costs, necessitating project re-structuring and financial net-zero designs.
Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwis…
We study the quasi-convergence equivalence of some families of metrics on locally homogeneous closed 4-manifolds with trivial isotropy group, and identify the dimension of each equivalence class under certain conditions.
We produce complete bounded curvature solutions to Kähler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth \K metric uniformly equivalent to another complete bounded curvature \K metric. We obtain related flow results for non-smooth as well as degenerate initial conditions. We a…
Synthetic Ricci flows defined for metric measure spaces.
problem Characterizing Ricci flows for non-smooth spaces.
method Heat flow, optimal transport, volume asymptotics.
result Equivalent characterizations of weighted Ricci flow.
Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circul…
Paper introduces new flows to find circle packings with specific curvature.
problem Finding circle packings with prescribed total geodesic curvatures.
method Introduces combinatorial Calabi flow, fractional combinatorial Calabi flow, and combinatorial p-th Calabi flow.
result Establishes conditions for the longtime behaviors of these flows.
We describe a calculus of moves for modifying a framed flow category without changing the associated stable homotopy type. We use this calculus to show that if two framed flow categories give rise to the same stable homotopy type of homological width at most three, then the flow categories are move equivalent. The proc…
Suppose the Riemannian metrics g and gˉ on a closed connected manifold Mn are geodesically equivalent and strictly non-proportional at least at one point. Then the topological entropy of the geodesic flow of g vanishes.