INNER TUBE FORMULAS FOR POLYTOPES

---

Copy For Citation

Kocak S., Ratiu A. V.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.140, no.3, pp.999-1010, 2012 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 140 Issue: 3
• Publication Date: 2012
• Doi Number: 10.1090/s0002-9939-2011-11307-8
• Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.999-1010
• Keywords: Polytope, Steiner formula, tube formula, SELF-SIMILAR TILINGS
• Anadolu University Affiliated: Yes

Abstract

We show that the volume of the inner r-neighborhood of a polytope in the d-dimensional Euclidean space is a pluriphase Steiner-like function, i.e. a continuous piecewise polynomial function of degree d, thus proving a conjecture of Lapidus and Pearse. We discuss also the degree of differentiability of this function and give a lower bound in terms of the set of normal vectors of the hyperplanes defining the polytope. We also give sufficient conditions for the highest differentiability degree to be attained.