{"paper":{"title":"The distance function from the boundary in a Minkowski space","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Malusa, G. Crasta","submitted_at":"2006-12-09T10:34:38Z","abstract_excerpt":"Let the space $\\mathbb{R}^n$ be endowed with a Minkowski structure $M$ (that is $M\\colon \\mathbb{R}^n \\to [0,+\\infty)$ is the gauge function of a compact convex set having the origin as an interior point, and with boundary of class $C^2$), and let $d^M(x,y)$ be the (asymmetric) distance associated to $M$. Given an open domain $\\Omega\\subset\\mathbb{R}^n$ of class $C^2$, let $d_{\\Omega}(x) := \\inf\\{d^M(x,y); y\\in\\partial\\Omega\\}$ be the Minkowski distance of a point $x\\in\\Omega$ from the boundary of $\\Omega$. We prove that a suitable extension of $d_{\\Omega}$ to $\\mathbb{R}^n$ (which plays the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612226","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"}