arXiv research

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.

The paper discusses fundamental problems in global Finsler geometry.

New method finds global Lagrangians for variational systems.

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.

The study proves non-existence theorems for Codazzi tensors on Riemannian manifolds.

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 study connects harmonic mappings to Ricci solitons.

Proves globally hyperbolic spacetimes via null distance completeness.

Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.

Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.

Estimates curvature and radius for constant mean curvature surfaces.

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…

Extends flat spacetimes with BTZ singularities, preserving key properties.

Invites into Alexandrov geometry with applications and theorems.

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 $(M,L)$ and the corresponding objects associated to $(M,\tilde{L})$, $\widetilde{L}=e^{σ(x)} L$ being the Finsl…

Synthetic proof shows globally hyperbolic Lorentzian spaces with specific curvature are warped products.

The paper examines the geometry of a curve's centre symmetry set.

String geometry theory connects strings to space-time and finds string vacua.

Surveying hermitian integral geometry, the paper describes new kinematic formulas for complex space forms.

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…

Study how local differential geometry affects global algebraic geometry of curves.

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 study finds sufficient conditions for Reeb flows to have genus zero global surfaces of section.

Study on biconservative surfaces in 3D space forms, focusing on complete surfaces.

Global covariance pooling improves deep CNNs' representation and generalization.

This work explores gradient flows and Riemannian structure in Gromov-Wasserstein geometry for data with global structure.

The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.

Study on geometry of Thurston metric on Teichmüller space.

Study how optimization methods' choices affect the solutions they find.

Study on manifolds with higher-rank lattice actions in projective and conformal classes.

Proposes integrating global and local entropy for more reliable LLMs.

Study proves existence of global solutions for Standard Model on expanding spacetimes.

This paper solves Hilbert's fourth problem for constant curvature metrics.

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…

Global regularity proved for 4D Ricci flow with scalar curvature integral bound.

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.

Introduces Anti-de Sitter geometry and its connection to Teichmüller theory.

New proof for global rigidity of vertex scaling on polyhedral surfaces.

The paper introduces new tests for global controllability in hybrid systems.

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.

Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.