A discrete extension of the Blaschke Rolling Ball Theorem - Mathematics > Differential GeometryReportar como inadecuado




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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|


Autor: Sz. Gy. Re've'sz

Fuente: https://arxiv.org/







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