Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature

Julià Cufí, Agustí Reventós

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2014, Masarykova Universita. All rights reserved. We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.
Original languageEnglish
Pages (from-to)219-236
JournalArchivum Mathematicum
Volume50
Issue number4
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Curvature
  • Evolutes
  • Gauss-Bonnet
  • Isoperimetric deficit

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