{"paper":{"title":"The Weil-Petersson curvature operator on the universal Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Yunhui Wu, Zheng Huang","submitted_at":"2018-05-23T12:39:31Z","abstract_excerpt":"The universal Teichm\\\"uller space is an infinitely dimensional generalization of the classical Teichm\\\"uller space of Riemann surfaces. It carries a natural Hilbert structure, on which one can define a natural Riemannian metric, the Weil-Petersson metric. In this paper we investigate the Weil-Petersson Riemannian curvature operator $\\tilde{Q}$ of the universal Teichm\\\"uller space with the Hilbert structure, and prove the following:\n  (i) $\\tilde{Q}$ is non-positive definite.\n  (ii) $\\tilde{Q}$ is a bounded operator.\n  (iii) $\\tilde{Q}$ is not compact; the set of the spectra of $\\tilde{Q}$ is n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09095","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"}