On Hadwiger's problem on inner parallel bodies
Volume 84 / 2009
Banach Center Publications 84 (2009), 121-129
MSC: Primary 52A20, 52A39; Secondary 52A40.
DOI: 10.4064/bc84-0-8
Abstract
We consider the problem of classifying the convex bodies in the 3-dimensional space depending on the differentiability of their associated quermassintegrals with respect to the one-parameter-depending family given by the inner/outer parallel bodies. It turns out that this problem is closely related to some behavior of the roots of the 3-dimensional Steiner polynomial.
