{"paper":{"title":"A M\\\"obius Characterization of Metric Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Thomas Foertsch, Viktor Schroeder","submitted_at":"2010-08-19T09:19:01Z","abstract_excerpt":"In this paper we characterize compact extended Ptolemy metric spaces with many circles up to M\\\"obius equivalence. This characterization yields a M\\\"obius characterization of the $n$-dimensional spheres $S^n$ and hemispheres $S^n_+$ when endowed with their chordal metrics. In particular, we show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is M\\\"obius equivalent to $(S^n,d_0)$ for some $n\\ge 1$, the $n$-dimensional sphere $S^n$ with its chordal metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3250","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"}