{"paper":{"title":"Poincar\\'e-Einstein 4-manifolds with cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Hongyi Liu, Mingyang Li","submitted_at":"2026-05-25T06:14:19Z","abstract_excerpt":"In this paper, we construct Poincar\\'e-Einstein 4-manifolds with various kinds of cusps. In particular, we construct:\n  (1) Infinite families of Einstein metrics on $(0,\\infty)\\times \\mathscr{N}$, where $\\mathscr{N}\\to T^2$ is a principal $\\mathbb{S}^1$-bundle over $T^2$, with one Poincar\\'e-Einstein end and one end asymptotic to a real or complex hyperbolic cusp.\n  (2) Infinite families of Einstein metrics on $(0,\\infty)\\times P$, where $P\\to \\Sigma_{\\mathtt{g}}$ is a principal $\\mathbb{S}^1$-bundle over a closed Riemann surface $\\Sigma_{\\mathtt{g}}$ of genus $\\mathtt{g}\\geq 2$, with one Poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25462","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25462/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"}