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.
Study of Teichmüller space geometry using infinitesimal and global methods.
Survey of global geometry for double field theory.
Global inverse function theorem proved easily using Riemannian geometry.
Study global geometry of toric nearly Kähler manifolds using multi-moment maps.
Study global geometry of dynamical systems with entire vector fields.
Researchers tackle the globalization problem of locally cosymplectic Hamiltonian dynamics.
Global homotopies upgrade classical map in differential geometry.
We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler manifold is so related to an integrable system. The cotangent bundle of a special …
The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this article, we introduce some important and fundamental topics in global Finsler geometry and discuss the related properties and the relationships in them. In particular, we optimize and improve the various definitions of …
Proves globally hyperbolic spacetimes via null distance completeness.
Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.
Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.
On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry o…
The aim of the present paper is to establish a global theory of conformal changes in Finsler geometry. Under this change, we obtain the relationships between the most important geometric objects associated to and the corresponding objects associated to , being the Finsl…
We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. These results will be obtained by using theorems of the connections between the geometry of a complete smooth manifold and the global behavio…
The paper examines the geometry of a curve's centre symmetry set.
Synthetic proof shows globally hyperbolic Lorentzian spaces with specific curvature are warped products.
String geometry theory connects strings to space-time and finds string vacua.
Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler manifold. To accomplish this, we introduce and investigate the notions of semispr…
We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.
In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a global point of view. We give an existence and uniqueness theorem for a remarkab…
Proves a synthetic Lorentzian Cartan-Hadamard theorem.
The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.
This work explores gradient flows and Riemannian structure in Gromov-Wasserstein geometry for data with global structure.
This work is based on the talk delivered at Poisson 2008. We review the recent advances in Generalized Kahler geometry while stressing the use of Poisson and symplectic geometry. The derivation of the generalized Kahler potential is sketched and the relevant global issues are discussed.
In a recent paper (arXiv:math-ph/0609076) the authors investigated the basic global geometry of congruence moduli curves and shape curves of 3-body motions with vanishing angular momentum. Here the study is extended to the case of planary 3-body motions in general. In particular, the results on the separation of the si…
Proposes integrating global and local entropy for more reliable LLMs.
This paper solves Hilbert's fourth problem for constant curvature metrics.
Study proves existence of global solutions for Standard Model on expanding spacetimes.
Global regularity proved for 4D Ricci flow with scalar curvature integral bound.
Introduces Anti-de Sitter geometry and its connection to Teichmüller theory.
The fermionic signature operator is analyzed on globally hyperbolic Lorentzian surfaces. The connection between the spectrum of the fermionic signature operator and geometric properties of the surface is studied. The findings are illustrated by simple examples and counterexamples.
New proof for global rigidity of vertex scaling on polyhedral surfaces.
Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{ü}ller space. We notice that Lorentzian generalisations of conical singularities are useful for the endeavours of desc…
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations.
Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.
We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We explore the question of whether the specifi…
We study collapsed manifolds with Ricci bounded covering geometry i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points. Via Ricci flows' techniques, we partially extend the nilpotent structural results of Cheeger-Fukaya-Gromov, on collapsed …
Survey on CR Paneitz operator and manifold embeddability.
The present paper is devoted to the study a global aspect of the geometry of harmonic mappings and, in particular, infinitesimal harmonic transformations, and represents the application of our results to the theory of Ricci solutions and the Ricci flow. These results will be obtained using the methods of Geometric anal…
We calculate relations on characteristic classes which are obstructions preventing closed Kähler manifolds from carrying holomorphic Cartan geometries. We apply these relations to give global constraints on the phase spaces of complex analytic determined and underdetermined systems of differential equations.
The exactness equation for Lepage 2-forms, associated with variational systems of ordinary differential equations on smooth manifolds, is analyzed with the aim to construct a concrete global variational principle. It is shown that locally variational systems defined by homogeneous functions of degree are …
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the {\it slope metric}. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic's behavior. A comparison between Finslerian and Riemannian areas of a bounded region is also studied.
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
Lorentzian Ptolemy inequality linked to curvature bounds.
I use harmonic maps and minimal surfaces to study quadratic equations in groups.
The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of …
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M …