A discrete extension of the Blaschke Rolling Ball Theorem - Mathematics > Differential GeometryReport as inadecuate




A discrete extension of the Blaschke Rolling Ball Theorem - Mathematics > Differential Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: The Rolling Ball Theorem asserts that given a convex body K in Euclideanspace and having a smooth surface bdK with all principal curvatures notexceeding c>0 at all boundary points, K necessarily has the property that toeach boundary point there exists a ball B r of radius r=1-c, fully contained inK and touching bdK at the given boundary point from the inside of K.In the present work we prove a discrete analogue of the result on the plane.We consider a certain discrete condition on the curvature, namely that to anyboundary points x,y with |x-y|


Author: Sz. Gy. Re've'sz

Source: https://arxiv.org/







Related documents