On the cut locus of submanifolds of a Finsler manifold (Q6611174)

The authors extend the results of [\textit{S. Basu} and \textit{S. Prasad}, Algebr. Geom. Topol. 23, No. 9, 4185--4233 (2023; Zbl 1534.53021)] to forward complete Finsler manifolds. Their main result is the following: let \((M,F)\) denote a Finsler manifold \(M\) with a forward complete Finsler metric \(F\), and \(N\) a closed submanifold of \(M\). If \(N\) is noncompact, then \(F\) is assumed to be backward complete. If \(\mbox{Cu}(N)\) denotes the cut locus of \(N\), then \(M\setminus \mbox{Cu}(N)\) strongly deformation retracts onto \(N\), and \(M\setminus N\) strongly deformation retracts onto \(\mbox{Cu}(N)\). In addition to these results, the authors give two characterisations of the cut locus; one in terms of the focal locus and the other in terms of the separating set.