2026-09-30T02:35:12Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25882 2026-09-23T23:53:33Z ddc:004 open_access

Geodesics of Length Less Than πR in a Set of Reach R Are Unique and Continuous with Respect to the Endpoints Lieutier, André Wintraecken, Mathijs Reach geodesics metric geometry Positive reach underpins many results in computational geometry and topology. It is used for triangulation criteria, topological inference, and manifold learning. The geometric properties of these sets have therefore been studied intensely. Here we focus on the shortest paths or minimizing geodesics in these sets. Our main result states that minimizing geodesics of length strictly less than π R in a set of reach R are unique. This in turn implies that such minimizing geodesics are continuous with respect to the endpoints. Schloss Dagstuhl – Leibniz-Zentrum für Informatik André Lieutier and Mathijs Wintraecken 2026 Is Part Of LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2026.75 urn:nbn:de:0030-drops-258823 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.75 eng https://creativecommons.org/licenses/by/4.0/legalcode