{"ID":2888828,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.22737","arxiv_id":"2507.22737","title":"On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime","abstract":"Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus ${\\cal NU}(M,g)$ of multiple maximizing geodesics on a globally hyperbolic spacetime $(M,g)$, i.e.\\ the set of causally related pairs $(x,y)$ for which there exists more than one maximizing geodesic (up to reparametrization) from $x$ to $y$. We will prove that this set is locally contractible. We will also define the notion of a Lorentzian Aubry set ${\\cal A}$ and prove that the inclusions ${\\cal NU}(M,g)\\hookrightarrow \\operatorname{Cut}_M\\hookrightarrow J^+\\backslash {\\cal A}$ are homotopy equivalences.","short_abstract":"Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus ${\\cal NU}(M,g)$ of multiple maximizing geodesics on a globally hyperbolic spacetime $(M,g)$, i.e.\\ the set of causally related pairs $(x,y)$ for which there exists more than one maximizing geodesic (up to reparam...","url_abs":"https://arxiv.org/abs/2507.22737","url_pdf":"https://arxiv.org/pdf/2507.22737v1","authors":"[\"Alec Metsch\"]","published":"2025-07-30T14:57:03Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math-ph\",\"math.DG\"]","methods":"[]","has_code":false}