Abstract

Lipschitz constants for the width and diameter functions of a convex body in Rn\mathbb{R}^n are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.

Author information

Contact details are reproduced from the original publication and may be historical.

Oleg Mushkarov

Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

muskarov@math.bas.bg

Nikolai Nikolov

(1) Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
(2) Faculty of Information Sciences, State University of Library Studies and Information Technologies, Sofia, Bulgaria

nik@math.bas.bg

Keywords

  • Convex body
  • diameter
  • width
  • thickness
  • Lipschitzness

Mathematics Subject Classification

52A20

References

  1. R. J. Gardner: Geometric Tomography, 2nd ed., Encyclopedia of Mathematics and its Applications 58, Cambridge University Press, New York (2006).Google Scholar
  2. H. Martini, L. Montejano, D. Oliveros: Bodies of Constant Width. An Introduction to Convex Geometry with Applications, Birkhäuser/Springer, Cham (2019).https://doi.org/10.1007/978-3-030-03868-7Google Scholar
  3. H. Martini, W. Wenzel: A Lipschitz condition for the width function of convex bodies in arbitrary Minkowski spaces, Appl. Math. Lett. 22 (2009) 142–145.https://doi.org/10.1016/j.aml.2007.12.032Google Scholar
  4. V. Soltan: Affine diameters of convex bodies – a survey, Expo. Math. 23 (2005) 47–63.https://doi.org/10.1016/j.exmath.2005.01.019Google Scholar

Suggested citation

O. Mushkarov, N. Nikolov, P. J. Thomas. “Lipschitzness of the Width and Diameter Functions of Convex Bodies in ℝ^n.” Journal of Convex Analysis 33 (2026), No. 1&2, 171–181. https://doi.org/10.68381/jca33011

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.