Argam Ohanyan

Almost-splitting of spacetimes under timelike sectional curvature bounds

Nicola Gigli, Melanie Graf, Robert J. McCann +3

We establish an almost-splitting theorem for spacetimes under timelike sectional curvature bounds in the spirit of the celebrated Riemannian result due to Cheeger and Colding. More…

Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime

Nicola Gigli, Argam Ohanyan, Marco Picerni +2

We study the directed completion of Lorentzian pre-length spaces, and we show that, under some natural assumptions which cover the case of smooth globally hyperbolic spacetimes, it…

Positive resolution of Bartnik's cosmological splitting conjecture

Robert J. McCann, Argam Ohanyan

We give a proof of the cosmological splitting conjecture of Robert Bartnik from 1988, which expresses the rigidity of the cosmological Hawking--Penrose singularity theorem. It stat…

Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations

Gregory J. Galloway, Robert J. McCann, Argam Ohanyan

The families of Lorentzian distance functions to and from points along a complete timelike line in a spacetime are known to be locally equi-Lipschitz continuous in a neighborhood o…

Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs

Argam Ohanyan, Marta Sálamo Candal

We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form $u \circ ℓ$ , where $u$ is a suitable m…

gr-qc2025

The Penrose singularity theorem, MOTS stability, and horizon topology in weighted spacetimes

Eric Ling, Argam Ohanyan, Eric Woolgar

We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbi…

Timelike conjugate points in Lorentzian length spaces

James D. E. Grant, Michael Kunzinger, Argam Ohanyan +2

We study notions of conjugate points along timelike geodesics in the synthetic setting of Lorentzian (pre-)length spaces, inspired by earlier work for metric spaces by Shankar--Sor…

math.MG2025

Topological cones and positively polarizable hyperbolic norms

Ethan Kharitonov, Argam Ohanyan

In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spa…

Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux

Miguel Manzano, Argam Ohanyan, Roland Steinbauer

The cut-and-paste method is a procedure for constructing null thin shells by matching two regions of the same spacetime across a null hypersurface. Originally proposed by Penrose,…

A Lorentzian splitting theorem for continuously differentiable metrics and weights

Mathias Braun, Nicola Gigli, Robert J. McCann +2

We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity $C^{1}$ by combining elliptic techniques for the negative homogeneity…

Distributional sectional curvature bounds for Riemannian metrics of low regularity

Darius Erös, Michael Kunzinger, Argam Ohanyan +1

Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandr…

math.DG2024★ 1 cited

Splitting theorems for weighted Finsler spacetimes via the $p$ -d'Alembertian: beyond the Berwald case

Erasmo Caponio, Argam Ohanyan, Shin-ichi Ohta

A timelike splitting theorem for Finsler spacetimes was previously established by the third author, in collaboration with Lu and Minguzzi, under relatively strong hypotheses, inclu…

An elliptic proof of the splitting theorems from Lorentzian geometry

Mathias Braun, Nicola Gigli, Robert J. McCann +2

We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We ex…

A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Tobias Beran, Mathias Braun, Matteo Calisti +5

We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the r…

gr-qc2024

Vacuum cosmological spacetimes without CMC Cauchy surfaces

Eric Ling, Argam Ohanyan

In this article, we extend a construction of [6] to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologi…

Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics

Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso

We study rigidity problems for Riemannian and semi-Riemannian manifolds with metrics of low regularity. Specifically, we prove a version of the Cheeger-Gromoll splitting theorem \c…