PreprintCC BY 4.0arXiv
Almost-splitting of spacetimes under timelike sectional curvature bounds
Abstract
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 concretely, we show that if a globally hyperbolic spacetime with timelike sectional curvature bounded below by a nonpositive constant close to zero contains a long maximizing timelike segment, then causal diamonds along that segment are close in the Lorentzian Gromov--Hausdorff sense of Minguzzi--Suhr to those in a product metric spacetime. Our result can be interpreted as a quantitative analogue of the Lorentzian splitting theorem for spacetimes with nonnegative timelike sectional curvature by Beem--Ehrlich--Markvorsen--Galloway.
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BibTeX
@misc{gigli2026almostsplitting,
title = {{Almost-splitting of spacetimes under timelike sectional curvature bounds}},
author = {Nicola Gigli and Melanie Graf and Robert J. McCann and Argam Ohanyan and Eric Woolgar and Matteo Zanardini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10051},
eprint = {2610.10051},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10051},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Almost-splitting of spacetimes under timelike sectional curvature bounds
AU - Nicola Gigli
AU - Melanie Graf
AU - Robert J. McCann
AU - Argam Ohanyan
AU - Eric Woolgar
AU - Matteo Zanardini
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10051
UR - https://arxiv.org/abs/2610.10051
AB - 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 concretely, we show that if a globally hyperbolic spacetime with timelike sectional curvature bounded below by a nonpositive constant close to zero contains a long maximizing timelike segment, then causal diamonds along that segment are close in the Lorentzian Gromov--Hausdorff sense of Minguzzi--Suhr to those in a product metric spacetime. Our result can be interpreted as a quantitative analogue of the Lorentzian splitting theorem for spacetimes with nonnegative timelike sectional curvature by Beem--Ehrlich--Markvorsen--Galloway.
ER -