{"paper":{"title":"Examples of Ricci limit spaces with infinite holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Shengxuan Zhou","submitted_at":"2024-03-31T09:16:47Z","abstract_excerpt":"Let $n\\geq 3$, $\\lambda \\in \\mathbb{R} $, and $(X,h)$ be an $n$-dimensional smooth complete Riemannian manifold with ${\\rm Ric}_h > \\lambda $.\n  In this paper, we construct, for each given $\\epsilon >0$, a sequence of $(n+2)$-dimensional manifolds $(M_{i} ,g_i ) \\stackrel{GH}{\\longrightarrow} (X_\\epsilon ,d_\\epsilon ) $ with ${\\rm Ric}_{g_i} > \\lambda $, such that $d_{GH} (X,X_\\epsilon ) \\leq \\epsilon $, and $X_\\epsilon $ is homeomorphic to the space obtained by removing an infinite number of balls from $X$. Hence $X_\\epsilon $ has dense boundary with an infinite number of connected components"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00619","kind":"arxiv","version":2},"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/2404.00619/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"}