arXiv research

New proof of Lorentzian splitting theorems using elliptic operators.

New splitting theorem for weighted Finsler spacetimes without Berwald condition.

We analyze Lorentzian spacetimes subject to curvature-dimension bounds using the Bakry-Émery-Ricci tensor. We extend the Hawking-Penrose type singularity theorem and the Lorentzian timelike splitting theorem to synthetic dimensions $N\le 1$, including all negative synthetic dimensions. The rigidity of the timelike spli…

Splitting theorem for non-positively curved Lorentzian spaces.

Paper proves new theorems about curvature in weighted manifolds.

Study Loday algebroids, prove splitting theorem, and linearize problems.

Low regularity spacetimes split into simpler structures.

New theorem splits weighted Lorentz-Finsler manifolds into simpler parts.

Sharp spectral theorem splits certain non-compact manifolds.

We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting result follows from an area comparison theorem for hypersurfaces with non-positi…

We prove a Lorentzian splitting theorem with weakened curvature conditions.

Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting theorem for Riemannian manifolds with singularities of nonnegative (Bakry-Emery…

New proof of splitting theorem and finite ends of minimal hypersurfaces in nonnegative curvature manifolds.

Synthetic splitting theorem for Lorentzian spaces with non-negative curvature.

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.

The aim of this paper is to prove a normal form Theorem for Dirac-Jacobi bundles using the recent techniques from Bursztyn, Lima and Meinrenken. As the most important consequence, we can prove the splitting theorems of Jacobi pairs which was proposed by Dazord, Lichnerowicz and Marle. As an application we provide a alt…

Short proof of Strong Haken Theorem for 3-manifolds.

We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.

The paper proves a theorem about splitting manifolds with specific curvature properties.

Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.

In this paper, I prove a splitting theorem for equifocal submanifolds with non-flat section in a simply connected symmetric space of compact type. Also, by using the splitting theorem, I prove that the sections of equifocal submanifolds with non-flat section in an irreducible simply connected symmetric space of compact…

The abstract proves a global splitting theorem for Poisson manifolds.

Abstract: Proves relative versions of group splitting results.

A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main theorem is: if N is a compact, connected, orientable 3-manifold …

We prove an almost splitting theorem for the warped product space with warped function $f(r)=\cosh\left(r\sqrt{\fracλ{n-2}}\right)$.

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.

In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group $Γ$ is said to be {\it rigid}, if $Γ$ determines the boundary up to homeomorphisms of a CAT(0) space on whi…

The paper explores rigidity and splitting theorems for sub-static spaces with minimal hypersurfaces.

The paper extends a splitting theorem for a specific type of tensor in Riemannian geometry.

Sharp eigenvalue bounds and splitting for modified Ricci flow.

The Bakry-Émery-Ricci tensor is extended and comparison theorems are proven.

The study proves splitting theorems for manifolds with specific curvature and boundary conditions.

In this paper, we prove two generalized versions of the Cheeger-Gromoll splitting theorem via the non-negativity of the Bakry-Émery Ricci curavture on complete Riemannian manifolds.

Researchers prove a 30-year-old cosmological conjecture about spacetime.

Unified proof of smooth fibration theorems for collapsed manifolds.

We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from below.

This paper generalizes Batchelor's theorem in $C^\infty$-superschemes.

We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature $Ric_f^m$ in timelike directions. We prove that they still hold when $m$ is finite, and when $m$ is infinite, they hold under the additional assumptio…

The paper proves manifold splitting theorems with nonnegative intermediate curvature.

In this paper we provide a classification theorem for 1-dimensional boundaries of groups with isolated flats. Given a group $Γ$ acting geometrically on a $CAT(0)$ space $X$ with isolated flats and 1-dimensional boundary, we show that if $Γ$ does not split over a virtually cyclic subgroup, then $\partial X$ is homeomorp…

Explains historical connections between vector bundle splitting and Riemann-Hilbert problems.

We investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger-Gromoll-Lichnerowicz splitting theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can pe…

The paper proves conditions for Einstein solitons to split into line and manifold.

Holomorphic splitting theorem for Calabi-Yau manifolds with specific properties.

New proof of Laudenbach and Poénaru's theorem on 4D 1-handlebodies.

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting theorem for the spectrum representing the cohomology theory of fold maps. For even q…

According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results are known e.g. for Lie algebroids, Dirac structures and generalized complex struc…

Develops a new inference method for split-sample estimators using multiple splits.