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.
The study finds all possible 3D polytopes in Riemannian 3-manifolds with positive scalar curvature.
We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.
Study contact 3-manifolds using sub-Riemannian geometry, proving new properties of their Lipschitz homotopy groups.
Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
Study proves rigidity of capillary surfaces in curved 3D spaces.
Study axisymmetric ideal fluids on 3-manifolds, proving Fredholm properties.
The simplicial volume of non-R^3 contractible 3-manifolds is infinite.
We show that open 3-manifolds that have a locally finite decomposition along 2-spheres are characterized by the existence of a Riemannian metric with respect to which the second homotopy group of the manifold is generated by small elements.
Study on 3-manifolds finds regular conformal metrics for rough metrics.
We obtain an exhaustive classification of totally umbilical surfaces in unimodular and non-unimodular simply-connected 3-dimensional Lie groups endowed with arbitrary left-invariant Riemannian metrics. This completes the classification of totally umbilical surfaces in homogeneous Riemannian 3-manifolds.
Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.
Let be an asymptotically flat Riemannian -manifold with non-negative scalar curvature and positive mass. We show that each leaf of the canonical foliation through stable constant mean curvature surfaces of the end of is uniquely isoperimetric for the volume it encloses.
We classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form into a surface.
We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.
Counterexamples found for volume entropy conjecture in hyperbolic 3-manifolds.
Study proves 3-manifolds with parallel vector fields have odd Betti numbers.
Geometric characterization of sub-Riemannian geodesics on frame bundles.
Classifies 3-manifolds with Killing vector fields, extending results from Riemannian to Lorentzian.
We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.
We apply the Riemannian Penrose inequality and the Riemannian positive mass theorem to derive inequalities on the boundary of a class of compact Riemannian -manifolds with nonnegative scalar curvature. The boundary of such a manifold has a CMC component, i.e. a -sphere with positive constant mean curvature; and t…
The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a divergence-free, constantly twisting, geodesic congruence. The shear of this congruence …
We study in detail the closed flat Riemannian 3-manifolds.
3-manifolds with convex boundary are rigid in certain curvature conditions.
Study eigenvalues of Laplace operator on specific 3D manifolds under Ricci flow.
A Killing submersion is a Riemannian submersion from an orientable 3-manifold to an orientable surface whose fibers are the integral curves of a unit Killing vector field in the 3-manifold. We classify all Killing submersions over simply-connected Riemannian surfaces and give explicit models for many Killing submersion…
Study classifies harmonic vector fields on 3-manifolds.
This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact geometry. Specifically, if a given three dimensional contact manifold (M,ξ) admits a …
3-manifolds with torsion homology expand in all dimensions.
Study on special symmetries in biwarped product 3-manifolds.
New proof shows certain 3D spaces are essentially like infinite space.
Alternative proof of flatness for Ricci-pinched 3-manifolds.
Study classifies 3-manifolds with constant Ricci eigenvalues.
There is a conjecture that a complete Riemannian 3-manifold with bounded sectional curvature, and pointwise pinched nonnegative Ricci curvature, must be flat or compact. We show that this is true when the negative part (if any) of the sectional curvature decays quadratically.
We study global obstructions to the eigenvalues of the Ricci tensor on a Riemannian 3-manifold. As a topological obstruction, we first show that if the 3-manifold is closed, then certain choices of the eigenvalues are prohibited: in particular, there is no Riemannian metric whose corresponding Ricci eigenvalues take th…
Paper bounds the sum of index and nullity of minimal surfaces in certain 3-manifolds.
Found a minimal surface in curved space.
Existence of non-trivial monopoles on 3-spheres proven.
We prove an L^2-estimate involving Ricci curvature and a harmonic 1-form on a closed oriented Riemannian 3-manifold admitting a solution of any rescaled Seiberg-Witten equations. We also give a necessary condition to be a monopole class on some special connected sums.
We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at least three with non-trivial fundamental groups and apply this result to the prime decomposition of a three-manifold. In particular we show…
New theorem on 3-manifolds with curvature and convex boundary.
We classify conformally flat Riemannian manifolds which possesses a free isometric action.
We define essential and strongly essential triangulations of 3-manifolds, and give four constructions using different tools (Heegaard splittings, hierarchies of Haken 3-manifolds, Epstein-Penner decompositions, and cut loci of Riemannian manifolds) to obtain triangulations with these properties under various hypotheses…
The paper bounds the -norm of Euler class for foliations on 3-manifolds.
We prove the existence of harmonic spinor fields in axisymmetric Riemannian 3-manifolds having nonnegative scalar curvature and asymptotic to the usual constant time hypersurface of Melvin's magnetic universe. Such a spinor can be used in the proof of the uniqueness of the magnetized Schwarzschild solution.
We apply an equivariant version of Perelman's Ricci flow with surgery to study smooth actions by finite groups on closed 3-manifolds. Our main result is that such actions on elliptic and hyperbolic 3-manifolds are conjugate to isometric actions. Combining our results with results by Meeks and Scott [17], it follows tha…
Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose sectional curvature is locally controlled and whose thick part becomes asymptotically hyperbolic and has a sufficiently small volume, then M is Seifert fibred or contains an inco…
Analytic Euler fields on non-torus bundles have periodic orbits.
For constant mean curvature surfaces of class immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of the ambient manifold, and the extrinsic shape of the surface. Then we prove classi…