A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves a theorem connecting graph theory spheres, reformulating Morse conditions.
Smooth approximations of Lipschitz maps via Ehresmann fibrations and Reeb sphere theorem for functions.
Smooth manifolds have functions with exactly two critical values.
The systolic ratio of a contact form on the three-sphere is the quantity \[ ρ_{\mathrm{sys}}(α) = \frac{T_{\min}(α)^2}{\mathrm{vol}(S^3,α\wedge dα)}, \] where is the minimal period of closed Reeb orbits on . A Zoll contact form is a contact form such that all the orbits of the corresponding R…
The study constructs K-contact manifolds with minimal closed Reeb orbits and provides conditions for their homeomorphism to spheres.
We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is Cohen-Macaulay, which is a generalization of equivariant formality for torus actions wi…
Study shows convex contact spheres resemble contact ellipsoids.
Study shows magnetic trajectories in Berger spheres are homogeneous.
The study finds at least two closed orbits for Reeb flows on certain contact manifolds.
We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS's. In particular, we generaliz…
The paper proves manifolds homeomorphic to spheres under specific Morse-Bott conditions.
The paper classifies 3D spherical Sasakian manifolds using geometric and algebraic methods.
The study restricts manifolds with certain explicit SGL maps and constructs them.
After observing that the well-known convexity theorems of symplectic geometry also hold for compact contact manifolds with an effective action of a torus whose Reeb vector field corresponds to an element of the Lie algebra of the torus, we use this fact together with a recent symplectic orbifold version of Delzant's th…
Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem cannot be obtained. We use an extension theorem for Kaehler geometry: given a compac…
We prove a version the local Reeb-Thurston stability theorem for symplectic foliations.
We give a dynamical characterisation of odd-dimensional balls within the class of all contact manifolds whose boundary is a standard even-dimensional sphere. The characterisation is in terms of the non-existence of short periodic Reeb orbits.
Study on knots and dynamics on three-sphere, linking bounds, and upper action bounds.
Study magnetic geodesics on odd spheres, computing critical energy values.
The paper characterizes Besse and Zoll Reeb flows on specific manifolds.
The paper characterizes contact 3-manifolds with closed Reeb orbits.
Study classifies Morse functions with 4 critical points on immersed 2-spheres.
Study of fold maps and Reeb spaces via surgery operations.
We survey some results on the existence (and non-existence) of periodic Reeb orbits on contact manifolds, both in the open and closed case. We place these statements in the context of Finsler geometry by including a proof of the folklore theorem that the Finsler geodesic flow can be interpreted as a Reeb flow. As a mil…
New method realizes planar graphs as Reeb graphs of algebraic functions.
The paper constructs contact-hyperbolic manifolds with large automorphism groups.
Quantizes contact structures using dynamical methods.
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…
On every compact, orientable, irreducible 3-manifold V which is toroidal or has torus boundary components we construct a contact 1-form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary. Moreover, if bdry V is nonempty, then the Reeb vector field R is transverse to …
Reeb flow made transverse to foliations without invariant measures.
Study shows Reeb orbits on starshaped hypersurfaces grow logarithmically with period.
The study finds sufficient conditions for Reeb flows to have genus zero global surfaces of section.
Study of Reeb spaces induced by generic maps, focusing on their homology groups.
We study invariant contact p-spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact p-spheres can only exist on (4n-1)-dimensional manifolds and we construct examples of contact p-spheres on such manifolds. We also consider relations between taut…
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…
Researchers reconstruct algebraic maps onto curves based on prescribed Reeb graphs.
The study uses symplectic capacities to bound the systole on the sphere.
3D contact forms have supporting decompositions, leading to entropy results.
New method constructs smooth functions for given Reeb graphs.
Inspired by Katok's examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic orbits. The first result is concerned with a contact-geometric description of magnetic flows on the 2-sphere found recently by Benedetti. We give a simple interpretat…
Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-component of the basic Euler class characterizes the existence of compatible Sasakian metrics for given small deformations of the Reeb flow as tra…
The paper studies the automorphisms of Kronrod-Reeb graphs for Morse functions on a 2-sphere.
We study on which compact Sasakian 3-manifolds the Reeb field, which is a Beltrami field with eigenvalue 2, is an energy minimizer in its adjoint orbit under the action of volume preserving diffeomorphisms. This minimization property for Beltrami fields is relevant because of its connections with the phenomenon of magn…
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).
The paper simplifies proofs and characterizes contact structures in 3D.
Study uses Newton polytopes to distinguish Lagrangian fillings of Legendrian submanifolds.
The study proves properties of spectral selectors for contact manifolds and applies them to contact big fibers and geodesics.
This thesis studies normal forms for Poisson structures around symplectic leaves using several techniques: geometric, formal and analytic ones. One of the main results (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric version of the Local Reeb Stability (from foliation theory) and…