{"paper":{"title":"A Maximum Problem of S.-T. Yau for Variational p-Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jie Xiao","submitted_at":"2013-02-20T21:35:21Z","abstract_excerpt":"Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in $\\mathbb R^{n\\ge 2}$ as an sharp upper bound of the variational $(1,n)\\ni p$-capacity radius, this paper settles a restriction/variant of S.-T. Yau's \\cite[Problem 59]{Yau} from the surface area to the variational $p$-capacity whose limit as $p\\to 1$ actually induces the surface area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5132","kind":"arxiv","version":6},"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"}