Tube volumes via functional equations

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DENİZ A., Koçak Ş., ÖZDEMİR Y., ÜREYEN A. E.

Journal of Geometry, vol.106, no.1, pp.153-162, 2015 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 106 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1007/s00022-014-0241-3
  • Journal Name: Journal of Geometry
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.153-162
  • Keywords: Tube formulas, self-similar sprays, functional equations, Mellin transform
  • Anadolu University Affiliated: Yes

Abstract

© 2014, Springer Basel AG.Tube formulas for convex sets and for smooth submanifolds of Euclidean spaces have long been of interest for geometers. In the last two decades there has been great progress on tube formulas for badly behaved spaces such as fractals, sprays and strings. We give a new, simple proof of an interesting tube formula of M. Lapidus and E. Pearse for self-similar sprays using a natural functional equation satisfied by tube volumes of them.