{"paper":{"title":"Degeneration of 3-dimensional hyperbolic cone structures with decreasing cone angles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Ken'ichi Yoshida","submitted_at":"2019-09-14T16:15:11Z","abstract_excerpt":"For 3-dimensional hyperbolic cone structures with cone angles $\\theta$, local rigidity is known for $0 \\leq \\theta \\leq 2\\pi$, but global rigidity is known only for $0 \\leq \\theta \\leq \\pi$. The proof of the global rigidity by Kojima is based on the fact that hyperbolic cone structures with cone angles at most $\\pi$ do not degenerate in deformations decreasing cone angles to zero.\n  In this paper, we give an example of a degeneration of hyperbolic cone structures with decreasing cone angles less than $2\\pi$. These cone structures are constructed on a certain alternating link in the thickened t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.06622","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.06622/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}