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.
Holomorphic vector bundles on Hopf manifolds admit flat connections.
The paper establishes a Poisson Poincaré-Dulac theorem for Poisson-flat connections.
New proofs for complex Hopf manifolds using geometric structures.
In this paper we address the following questions: (i) Let be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is contained in an algebraic curve? (ii) What can be said of a polynomial vector field which has a finitely curved transcendent orbit? We give a positi…
Proves Poincaré surgery theorem using homotopy theory.
Proves a theorem for 3D Poincaré duality pairs.
The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
Generalizes Poincaré-Hopf Theorem for piecewise smooth boundaries.
Extends Poincaré-Lefschetz duality to pairs of ∞-categories.
We prove two kinds of fibering theorems for maps X --> P, where X and P are Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue of the fibering theorem of Browder and Levine.
A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions . In 1984 Jänich presented a Poincaré-Hopf th…
Poincaré's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discreteness of groups of isometries. This work contains a version of Poincaré's Polyhedron Theorem that is applicable to constructing fibre bund…
Study proves rigidity and gap theorems for specific metrics.
In this paper we prove type gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincaré inequality. We apply the theorems to a broad class of complete manifolds satisfying weighted Poincaré inequalities. In particular, we obtain a gap theorem on the Euclidean space wi…
The study examines stability and instability of Poincaré-Einstein metrics using Ricci flow.
We state and prove a generalization of the Poincaré-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.
Paper uses algebraic methods to prove an equivariant Poincaré-Hopf theorem.
Liouville theorem for minimal graphs on manifolds with specific properties.
Fiedler and Mallet-Paret prove a version of the classical Poincaré-Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of the non-linear Cauchy-Riemann equations. The latter is an application of an abstract theorem for flows with a(n) (unbounded) discrete Lyapuno…
We prove a version of the Arezzo-Pacard-Singer blow-up theorem in the setting of Poincaré type metrics. We apply this to give new examples of extremal Poincaré type metrics. A key feature is an additional obstruction which has no analogue in the compact case. This condition is conjecturally related to ensuring the metr…
Completes reduction scheme in Lagrange-Poincaré category.
Poincaré-Hopf theorem extended to Filippov vector fields on 2D manifolds.
We treat the Witten operator on the de Rham complex with semiclassical heat kernel methods to derive the Poincaré-Hopf theorem and degenerate generalizations of it. Thereby, we see how the semiclassical asymptotics of the Witten heat kernel are related to approaches using the Thom form of Mathai and Quillen.
New theorem proves rigidity of circle packings in hyperbolic geometry.
Uniform Poincaré inequalities established for various metric spaces.
For a manifold with boundary, the restriction of Chern's transgression form of the Euler curvature form over the boundary is closed. Its cohomology class is called the secondary Chern-Euler class and used by Sha to formulate a relative Poincaré-Hopf theorem, under the condition that the metric on the manifold is locall…
The goal of this work is to generalize the Gauss-Bonnet and Poincaré-Hopf Theorems to the case of orbifolds with boundary. We present two such generalizations, the first in the spirit of Satake. In this case, the local data (i.e. integral of the curvature in the case of the Gauss-Bonnet Theorem and the index of the vec…
A geometric version of the Poincaré Lemma is established for the topological vector space of differential chains. In particular, every differential k-cycle with compact support in a contractible open subset U of a smooth n-manifold M is the boundary of a differential (k+1) -chain with compact support in U. Applications…
We prove a version of Poincaré's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can be generalized to the case of higher dimension and other geometric structures. It …
Geometrization Theorem solves complex geometry problems.
The purpose of this mostly expository paper is to discuss a connection between Nielsen fixed point theory and symplectic Floer homology theory for symplectomorphisms of surface and a calculation of Seidel's symplectic Floer homology for different mapping classes. We also describe symplectic zeta functions and asympltot…
The study determines lens spaces that can be obtained from surgeries on knots in the Poincaré homology sphere.
We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincaré inequality. In the process, a sharp decay estimate for the minimal positive Green's function is obtained. This estimate only depends on the weight function of the Poincaré inequality, and yields …
The study proves rigidity for Poincaré-Einstein manifolds with flat Euclidean conformal infinity.
New proof of surface group theorem for 2D Poincaré duality groups.
After analyzing renormalization schemes on a Poincaré-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior und…
The paper explores the geometry of holomorphic flows and orbits.
Paper extends Poincaré's work to stochastic differential equations.
The paper extends Thurston's method to new variants of Mather-Thurston theorem.
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincaré-Cartan form. Noether theorem and examples from superfi…
We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincaré metrics, this leads to a natural extension of the notion of Branson's -curvature to Weyl structures on even-dimension…
Paper proves existence of a CMC hypertorus in 4D sphere using numerical methods.
Proves 3D Poincaré duality groups without property (T)
Study vector fields on non-compact manifolds with group action.
The paper proves a Liouville theorem for special Lagrangian equations with convexity conditions.
We show that both, the Jordan curve theorem and the Schoenflies theorem extend to non-metric manifolds (at least in the two-dimensional context), and conclude by some dynamical applications à la Poincaré-Bendixson.
This paper is a continuation of the paper F. A. Arias and M. Malakhaltsev "A generalization of the Gauss-Bonnet and Hopf-Poincaré theorems", ArXiv:1510.01395 [MathDG] 5 Oct 2015. Let be a locally trivial fiber bundle over a two-dimensional manifold , and be a discrete subset. A subset $Q \s…