We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.
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This paper classifies instantons with closed reductions and provides examples of non-closed reductions.
problem Understanding the geometry of toric Kähler instantons with and without closed reductions.
method Sharp geometric criteria and examples of instantons with different reduction types.
result Established geometric criteria for closed reductions and classified asymptotic geometries.
No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.
problem Proving the nonexistence of closed timelike geodesics in Kerr spacetimes.
method Analyzing the Kerr-star spacetime, excluding closed null geodesics and proving the nonexistence of closed timelike geodesics.
result No closed timelike geodesics in Kerr spacetimes.
The paper characterizes simple closed curves on surfaces using profinite rigidity.
problem Characterizing simple closed curves on surfaces using profinite rigidity.
method Proving that elements with the same images under all finite groups are simple closed curves.
result The set of simple closed curves is closed in the profinite topology of the surface group.
The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closedmath.SG
The paper characterizes contact 3-manifolds with closed Reeb orbits.
problem Characterizing contact 3-manifolds with closed Reeb orbits.
method Analyzing the action spectrum and minimal periods of Reeb orbits.
result A contact form with an action spectrum of rank 1 is uniquely determined by the minimal periods of its closed Reeb orbits.
Topological complexity for closed 1-forms
problem Topological complexity for closed 1-forms
method Introduce and study a corresponding version of topological complexity
result Establish analogues of basic properties of ordinary topological complexity
Study on -structures with negative Ricci curvature on closed and noncompact manifolds.
problem Existence and properties of closed -structures with negative Ricci curvature.
method Analyzing existence and nonexistence of closed -structures with negative Ricci curvature on closed and noncompact manifolds.
result No closed manifold admits a closed -structure with negative Ricci curvature. For noncompact manifolds, restrictions on lengths of geodesics are found.
Proves stability of geodesic flows on closed surfaces.
problem Stability of geodesic flows on closed surfaces.
method Generic Riemannian metrics and Reeb flows.
result Proves -stability conjecture for geodesic flows.
Study shows compact Lorentz manifolds can't have closed geodesics.
problem Existence of closed geodesics in compact Lorentz manifolds.
method Constructed compact Lorentz manifolds without closed geodesics.
result Compact Lorentz manifolds can't have closed geodesics.
The study classifies spaces with specific conformal vector fields.
problem Characterizing closed vacuum static spaces with non-Killing conformal vector fields.
method Provided characterizations and established an identity involving the characteristic function.
result Derived a rigidity theorem and classified spaces with the vector field.
This paper adresses the following problem: Given a closed orientable three-manifold M, are there at most finitely many closed orientable three-manifolds 1-dominated by M? We solve this question for the class of closed orientable graph manifolds. More presisely the main result of this paper asserts that any closed orien…
Kerr spacetimes without closed null geodesics for non-zero rotation.
problem Analyzing closed geodesics in Kerr spacetimes.
method Analytic extension and geodesic analysis.
result Kerr spacetimes do not admit closed null geodesics for any non-zero rotation parameter.
Adjusted Closing Pricesq-fin.PM
Historical returns depend on historical closing prices and distributions. We describe how to compute adjusted closing prices from closing price/distribution data with an emphasis on spreadsheet implementation. Then the growth of a security from one date to another (1 + total return) is just the ratio of the correspondi…
If all prime closed geodesics on with an irreversible Finsler metric are irrationally elliptic, there exist either exactly or infinitely many distinct closed geodesics. As an application, we show the existence of three distinct closed geodesics on bumpy Finsler if a…
2-stratifold spines list all closed 3-manifolds.
problem Classifying closed 3-manifolds using 2-stratifold spines.
method Using 2-stratifold spines to list all closed 3-manifolds.
result Listed all closed 3-manifolds with 2-stratifold spines.
Proves h-principle for symplectic foliations on closed manifolds.
problem Symplectic foliations on closed manifolds.
method Proves h-principle for regular symplectic foliations.
result Establishes h-principle for symplectic foliations on closed manifolds.
Classifies closed surface braids up to isotopy and homeomorphism.
problem Classifying closed surface braids up to isotopy and homeomorphism.
method Algebraic classification using surface braid group and mapping class group actions.
result Braids close to isotopic or homeomorphic links if and only if they are conjugate or in the same orbit of the outer action of the mapping class group.
The paper proves the existence of multiple closed geodesics on certain Finsler manifolds.
problem Proving the existence of multiple closed geodesics on positively curved Finsler manifolds.
method Analyzing Finsler manifolds with specific curvature conditions to prove the existence of closed geodesics.
result On Finsler manifolds with certain curvature conditions, there exist multiple closed geodesics.
The study reveals conditions for infinite closed geodesics on specific surfaces.
problem Conditions for infinite closed geodesics on complete surfaces.
method Analyzes geometric and homological properties of closed geodesics on cylinders and planes.
result Proves that complete cylinders with isolated geodesics have zero, one, or infinitely many homologically visible geodesics.
The paper studies the shortest closed multi-geodesics on hyperbolic surfaces as their genus grows.
problem Finding the asymptotic behavior of shortest closed multi-geodesics on hyperbolic surfaces.
method Analyzing the length of shortest filling closed multi-geodesics using hyperbolic geometry and asymptotic analysis.
result The length of a shortest filling closed multi-geodesic is uniformly comparable to a specific formula involving the genus and lengths of closed geodesics.
This article deals with a continuous closed 1-form defined on a CW-complex. In particular, we show Lusternik-Schnirelmann type theory on continuous closed 1-forms which is related to gradient-like flows. M.Farber defined a continuous closed 1-form and a category with a respect to a cohomology class and constructed a Lu…
In this note we establish estimates for the harmonic map heat flow from into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic.
New theorem on geodesics on non-compact manifolds.
problem Existence of geodesics with specific properties.
method Analyzing geodesics with local homology in maximal degree.
result Infinitely many closed geodesics on non-compact manifolds.
A quantitative closing Lemma and Partner orbits on Riemannian manifolds with negative curvaturemath.DG
Proves a quantitative closing lemma for negatively curved manifolds.
problem Closing lemma for negatively curved manifolds.
method Quantitative closing lemma proof.
result Study of partner and pseudo-partner orbits for self-crossing closed geodesics.
Closed finite gap curves are dense in Sobolev spaces of curves in hyperbolic and Euclidean 3-spaces.
problem Density of closed finite gap curves in Sobolev spaces.
method Proof of density in Sobolev spaces for curves in hyperbolic and Euclidean 3-spaces.
result Closed finite gap curves are dense in Sobolev spaces of curves in hyperbolic and Euclidean 3-spaces.
Characterizes covers using simple closed curves on surfaces.
problem Tackles the equivalence of covers via simple closed curves.
method Uses Teichmüller theory and the complex of curves.
result Two covers are equivalent if and only if the same curves lift to simple curves.
The study finds the number of closed geodesics on a specific type of manifold.
problem Determining the number of closed geodesics on a manifold with elliptic prime geodesics.
method Analyzes a compact manifold with a specific cohomology structure and a bumpy Finsler metric.
result There are either exactly or distinct closed geodesics, or infinitely many.
Smart Close-out Nettingq-fin.RM
Smart Close-out Netting aims to automate close-out netting processes.
problem Inefficiencies in close-out netting processes for financial institutions.
method Standardisation and automation of legal and regulatory processes using a data-driven framework and controlled natural language.
result Standardisation and automation can improve close-out netting processes for prudentially regulated financial institutions.
We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of the flow. In the other subset every closed orbit is freely homotopic to only one …
In the recent paper \cite{LoD1}, we classified closed geodesics on Finsler manifolds into rational and irrational two families, and gave a complete understanding on the index growth properties of iterates of rational closed geodesics. This study yields that a rational closed geodesic can not be the only closed geodesic…
Survey on strong closing lemmas in Hamiltonian dynamics.
problem Understanding dynamics in Hamiltonian systems.
method Use spectral invariants in symplectic geometry.
result Proofs of strong closing lemmas in various dimensions.
Closed curves in 3D and 4D spheres are dense in Sobolev norms.
problem Characterizing closed curves in 3D and 4D spheres.
method Density in Sobolev -norm.
result Spaces of closed finite gap curves are dense in the spaces of closed curves.
We consider the closed orbit structure of generic gradient flows of Morse closed 1-forms. The torsion of a chain homotopy equivalence between the Novikov complex and the completed simplicial chain complex of the universal cover detects the eta function of the flow. We extend this result to arbitrary Morse closed 1-form…
The paper proves new Hardy inequalities on closed manifolds using Ricci curvature.
problem Proving Hardy inequalities on closed manifolds.
method Using various weighted Ricci curvatures.
result Sharp Hardy type inequalities established on closed weighted Riemannian manifolds.
Closed ray affine manifoldsmath.DG
Study closed manifolds with rank one ray structures, proving completeness or covering properties.
problem Characterize closed manifolds with specific affine structures.
method Analyze the developing map and automorphism group properties.
result Closed manifolds with rank one ray structures are either complete or cover the complement of an affine subspace.
Shortest non-simple closed geodesics on hyperbolic surfaces found.
problem Finding the shortest non-simple closed geodesics on hyperbolic surfaces.
method Analyzing closed geodesics with at least k self-intersections on hyperbolic surfaces.
result The shortest non-simple closed geodesics lie on an ideal pair of pants and have length $2\arccosh(2k+1)$.
The paper proves a conjecture about the minimum number of closed geodesics on a Finsler 3-sphere.
problem Proving the Anosov conjecture for bumpy Finsler 3-spheres.
method Analyzing the Morse index of prime closed geodesics.
result Established the conjecture for Finsler 3-spheres with nonzero Morse index.
Proof shows Chern form is closed on groupoid convolution algebra.
problem Proving the Chern form's closedness on étale groupoids.
method Used bisection for algebraic proof.
result Chern form is closed on étale groupoid convolution algebra.
Study constructs closed curves with constant curvature on cylinders and tori.
problem Creating closed curves with constant curvature.
method ODEs and symmetry arguments, starting with cylinders, then tori, and finally Frenet-Serret equations.
result Closed constant curvature space curves constructed on cylinders and tori.
Study on minimizing closed geodesics on polygons and disks.
problem Understanding and minimizing closed geodesics on polygons and disks.
method Developed new techniques to study minimizing properties of 1/k geodesics on doubled polygons.
result Demonstrated a sequence of doubled polygons whose closed geodesics exhibit unbounded minimizing properties.
Study geodesics on spherical polyhedra, estimating their number.
problem Counting simple closed geodesics on spherical polyhedra.
method Examined regular spherical octahedra, cubes, and tetrahedra.
result Estimated the number of simple closed geodesics on spherical polyhedra.
Stability of Convex Spheresmath.DG
Proves stability of convex spheres with similar geodesic lengths.
problem Stability of convex spheres with specific geodesic properties.
method Proves C^0 Cheeger-Gromov closeness to the round sphere.
result Strictly convex 2-spheres are close to the round sphere.
In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is L…
We show that every closed Lorentzian surface contains at least two closed geodesics. Explicit examples show the optimality of this claim. Refining this result we relate the least number of closed geodesics to the causal structure of the surface and the homotopy type of the Lorentzian metric.
We prove Calegari's conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold has closed orbits.
Constructs a function to count closed geodesics on Riemannian manifolds.
problem Counting closed geodesics on Riemannian manifolds.
method Defines a locally constant geodesic count function and investigates the weight of compact open subsets of closed geodesics.
result Constructs a function to count closed geodesics on Riemannian manifolds.
If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form which linearly deforms into contact forms, then M supports a K-contact form. On the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if and only if it is a fibration 1-form. on any other 2-torus bundle over the circle, ev…
The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.
problem Finding prime closed characteristics on compact star-shaped hypersurfaces in 8D space.
method Proved existence of at least four prime closed characteristics for non-degenerate compact star-shaped hypersurfaces in without prime closed characteristics of Maslov-type index -1.
result Existence of at least four prime closed characteristics on compact star-shaped hypersurfaces in .