{"paper":{"title":"Criterions of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schr\\\"odinger operator in a cone","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Guantie Deng, Pinhong Long, Zhiqiang Gao","submitted_at":"2012-05-28T11:35:34Z","abstract_excerpt":"In the paper we give some criterions for a-minimally thin sets and a-rarefied sets associated with the stationary Schr\\\"odinger operator at a fixed Martin boundary point or {\\infty} with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside a-rarefied set. Finally we illustrate the relation between a-minimally thin set and a-rarefied set in a cone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6081","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"}