Splitting and pinching for convex sets

✍ Scribed by Peter Kohlmann

• Book ID: 104649248
• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 917 KB
• Volume: 60
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00160618

✦ Synopsis

We consider noncompact, closed and convex sets with nonvoid interior in Euclidean space. It is shown that if such a set has one curvature measure sufficiently close to the boundary measure, then it is congruent to a product of a vector space and a compact convex body. Related stability and characterization theorems for orthogonal disc cylinders are proved. Our arguments are based on the Steiner-Schwarz symmetrization processes and generalized Minkowski integral formulas.