{"paper":{"title":"On $L^p$-Liouville property for smooth metric measure spaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jia-Yong Wu, Peng Wu","submitted_at":"2014-10-27T16:48:23Z","abstract_excerpt":"In this short paper we study $L_f^p$-Liouville property with $0<p<1$ for nonnegative $f$-subharmonic functions on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with $\\mathrm{Ric}_f^m$ bounded below for $0<m\\leq\\infty$. We prove a sharp $L_f^p$-Liouville theorem when $0<m<\\infty$. We also prove an $L_f^p$-Liouville theorem when $\\mathrm{Ric}_f\\geq 0$ and $|f(x)|\\leq \\delta(n) \\ln r(x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7305","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"}