A general geometric construction for affine surface area

1997/06/30 by Elisabeth M. Werner, Werner, Elisabeth
Mathematics · #52A38 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/9706215

openalex publication_date 1997/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a convex body in \bf Rⁿ and B be the Euclidean unit ball in \bf Rⁿ. We show that lim_{t→ 0} (|K| -|K_t|)/(|B| - |B_t|)= (as(K))/(as(B)), where as(K) respectively as(B) is the affine surface area of K respectively B and \K_t\_{t≥ 0}, \B_t\_{t≥ 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].

Related

• On the p-affine surface area
• Constrained convex bodies with extremal affine surface areas
• Floating bodies for ball-convex bodies
• Some inequalities of isoperimetric type for the c-affine surface area
• Ball-convex bodies and L_p relative surface areas