{"paper":{"title":"Closed strong spacelike curves, Fenchel theorem and Plateau problem in the 3-dimensional Minkowski space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nan Ye, Xiang Ma","submitted_at":"2016-03-25T01:03:12Z","abstract_excerpt":"We generalize the Fenchel theorem for strong spacelike closed curves of index $1$ in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to $2\\pi$. Here strong spacelike means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve $\\gamma$ under consideration. The assumption of index 1 is equivalent to saying that $\\gamma$ winds around some timelike axis with winding number 1. We prove this reversed Fenchel-type inequality by constructing a ruled spacelike surface with the given curve as boundary and apply"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07793","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}