{"paper":{"title":"On the Gromov-Hausdorff limits of Tori with Ricci conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shengxuan Zhou","submitted_at":"2023-09-20T01:37:46Z","abstract_excerpt":"Let $n\\geq 4$. In this paper, we construct a sequence of smooth Riemannian metrics $g_i $ on $\\mathbb{R}^n$ such that: (1) $g_i = g_{\\rm Euc} $ outside the standard Euclidean unit ball $B_1 (0) \\subset \\mathbb{R}^n $, (2) ${\\rm Ric}_{g_i} \\geq -\\Lambda $ and $ {\\rm diam} \\left( B_1 (0) ,g_i \\right) \\leq D $ for some $\\Lambda ,D>0$ independent of $i$, (3) The pointed Gromov-Hausdorff limit of $(\\mathbb{R}^n ,g_i) $ is a topological orbifold but not a topological manifold.\n  As a consequence, for $n\\geq 4$, we can find a sequence of tori $(T^n , g_i )$ with Ricci lower bound and diameter bound s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.10997","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/2309.10997/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"}