Nonbranching under curvature bounds for low-regularity Finsler structures

Determine whether curvature bounds imply nonbranching for low-regularity Finsler structures.

Background

The paper establishes Hawking and Penrose singularity theorems for low-regularity Lorentz–Finsler structures, where geodesics need not be uniquely determined by their initial conditions and branching is therefore not excluded. The authors contrast their approach with synthetic singularity theorems based on optimal transport, which require a nonbranching condition. They explicitly identify the unresolved issue of whether curvature bounds themselves enforce nonbranching in the low-regularity Finsler setting.

References

As for low regularity Finsler structures, it is unclear if curvature bounds imply nonbranching (cf. ), hence our theorems would not be subsumed by their synthetic counterparts .

— The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes  (2610.11911 - Erös et al., 8 Oct 2026) in Introduction, paragraph beginning “Let us remark that, in the case of $C^1$ Lorentzian metrics...”