{"paper":{"title":"The Wulff construction for convex integrands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Huhe Han, Takashi Nishimura","submitted_at":"2016-07-11T10:12:35Z","abstract_excerpt":"For any given Wulff shape $\\mathcal{W}$, we can define the unique continuous function $S^{n}\\to \\mathbb{R}_{+}$ called convex integrand, denoted by $\\gamma_{{}_{\\mathcal{W}}}$. In this paper, we show that, for any Wulff shapes $\\mathcal{W}_{1}$ and $\\mathcal{W}_{2}$, the equality $d(\\gamma_{{}_{\\mathcal{W}_{1}}}, \\gamma_{{}_{\\mathcal{W}_{2}}})= h(\\mathcal{W}_{1}, \\mathcal{W}_{2})$ holds, where $d$ is the maximum distance of the function space consisting of convex integrands and $h$ is the Pompeiu-Hausdorff distance of the space consisting of Wulff shapes. Moreover, applications of this result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02885","kind":"arxiv","version":3},"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"}