INNER TUBE FORMULAS FOR POLYTOPES

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Kocak S., Ratiu A. V.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.140, sa.3, ss.999-1010, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 140 Sayı: 3
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1090/s0002-9939-2011-11307-8
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.999-1010
  • Anahtar Kelimeler: Polytope, Steiner formula, tube formula, SELF-SIMILAR TILINGS
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.