{"paper":{"title":"A general geometric construction for affine surface area","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Elisabeth Werner","submitted_at":"1997-06-30T00:00:00Z","abstract_excerpt":"Let $K$ be a convex body in ${\\bf R}^n$ and $B$ be the Euclidean unit ball in ${\\bf R}^n$. We show that $$\\mbox{lim}_{t\\rightarrow 0} \\frac{|K| -|K_t|}{|B| - |B_t|}= \\frac{as(K)}{as(B)},$$ where $as(K)$ respectively $as(B)$ is the affine surface area of $K$ respectively $B$ and $\\{K_t\\}_{t\\geq 0}$, $\\{B_t\\}_{t\\geq 0}$ are general families of convex bodies constructed from $K$, $B$ satifying certain conditions. As a corollary we get results obtained in [M-W], [Schm],[S-W] and[W]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9706215","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"}