Skip to main content

Comparing the relative volume with the relative inradius and the relative width

Abstract

We consider subdivisions of a convex body in two subsets and. We obtain several inequalities comparing the relative volume: (1) with the minimum relative inradius, (2) with the maximum relative inradius, (3) with the minimum relative width, and (4) with the maximum relative width. In each case, we obtain the best upper and lower estimates for subdivisions determined by general hypersurfaces and by hyperplanes.

[12345]

References

  1. 1.

    Cerdán A, Miori C, Segura Gomis S: Relative isodiametric inequalities. Beiträge zur Algebra und Geometrie 2004,45(2):595–605.

    MATH  Google Scholar 

  2. 2.

    Cerdán A, Schnell U, Segura Gomis S: On relative geometric inequalities. Mathematical Inequalities & Applications 2004,7(1):135–148.

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Cianchi A: On relative isoperimetric inequalities in the plane. Bollettino della Unione Matemàtica Italiana. Serie VII. B 1989,3(2):289–325.

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Pál J: Ein Minimumproblem für Ovale. Mathematische Annalen 1921,83(3–4):311–319. 10.1007/BF01458387

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Peri C: On relative isoperimetric inequalities. Conferenze del Seminario di Matematica dell'Università di Bari 2001, (279):14.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. Cerdán.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Cerdán, A. Comparing the relative volume with the relative inradius and the relative width. J Inequal Appl 2006, 54542 (2006). https://doi.org/10.1155/JIA/2006/54542

Download citation

Keywords

  • Relative Volume
  • Convex Body
  • Lower Estimate
  • Relative Width
  • General Hypersurface
\