{"paper":{"title":"Localization results for Minkowski contents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Steffen Winter","submitted_at":"2016-10-10T22:32:00Z","abstract_excerpt":"It was shown recently that the Minkowski content of a bounded set $A$ in $\\mathbb{R}^d$ with volume zero can be characterized in terms of the asymptotic behaviour of the boundary surface area of its parallel sets $A_r$ as the parallel radius $r$ tends to $0$. Here we discuss localizations of such results. The asymptotic behaviour of the local parallel volume of $A$ relative to a suitable second set $\\Omega$ can be understood in terms of the suitably defined local surface area relative to $\\Omega$. Also a measure version of this relation is shown: Viewing the Minkowski content as a locally dete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03117","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"}