Convergence of Lorentzian spaces and curvature bounds for generalized cones
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914555850915840 |
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| author | Ketterer, Christian |
| author_facet | Ketterer, Christian |
| contents | The goal of this article is twofold. We introduce a notion of convergence for Lorentzian pre-length spaces, $\ell$-convergence, that extends previous convergence notions in this context. We show that timelike curvature and timelike curvature-dimension bounds are stable under (measured) $\ell$-convergence. Then, we show that $\ell$-convergence is well adapted for generalized Lorentzian cones: a sequence of generalized cones $-I_i\times_{f_i}X_i$ converges in $\ell$ sense if the base $I_i$ and the fiber $X_i$ converge in GH sense and the functions $f_i$ converge uniformly. We use this to show sharp timelike curvature and timelike curvature-dimension bounds for such cones. Finally, we obtain a pre-compactness theorem for $\ell$-convergence in the class of smooth generalized cones that have a uniform lower bound on the full Ricci (or Riemann) curvature tensor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11271 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence of Lorentzian spaces and curvature bounds for generalized cones Ketterer, Christian Differential Geometry Mathematical Physics Metric Geometry The goal of this article is twofold. We introduce a notion of convergence for Lorentzian pre-length spaces, $\ell$-convergence, that extends previous convergence notions in this context. We show that timelike curvature and timelike curvature-dimension bounds are stable under (measured) $\ell$-convergence. Then, we show that $\ell$-convergence is well adapted for generalized Lorentzian cones: a sequence of generalized cones $-I_i\times_{f_i}X_i$ converges in $\ell$ sense if the base $I_i$ and the fiber $X_i$ converge in GH sense and the functions $f_i$ converge uniformly. We use this to show sharp timelike curvature and timelike curvature-dimension bounds for such cones. Finally, we obtain a pre-compactness theorem for $\ell$-convergence in the class of smooth generalized cones that have a uniform lower bound on the full Ricci (or Riemann) curvature tensor. |
| title | Convergence of Lorentzian spaces and curvature bounds for generalized cones |
| topic | Differential Geometry Mathematical Physics Metric Geometry |
| url | https://arxiv.org/abs/2605.11271 |