Skip to main content
SpringerLink
Log in

Asymmetry for convex body of revolution

  • Mathematics
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

In this paper, we study the Minkowski measure of asymmetry for n-dimensional convex bodies of revolution ( n⩾3 ). We show that among all n-dimensional convex bodies of revolution, the bodies which generated by isosceles triangles are the most asymmetric ones. Also, we study the asymmetry for n-dimensional constant width bodies of revolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Grunbaum B. Measure of symmetry for convex sets [C]// Convexity Proceedings of Symposia in Pure Mathematics 7. Providence: American Math Society, 1963: 233–270.

    Google Scholar 

  2. Ekstrom E. The critical set of a convex body [EB/OL]. [2014-03 20].http://www2.math.uu.se/research/pub/preprints.php#exjobb.

  3. Groemer H. Stability theorems for two measures of symmetry [J]. Discrete Comput Geom, 2000, 24: 301–311.

    Article  Google Scholar 

  4. Guo Q. Stability of the Minkowski measure of asymmetry for convex bodies [J]. Discrete Comput Geom, 2005, 34: 351–362.

    Article  Google Scholar 

  5. Guo Q. On p-measures of asymmetry for convex bodies [J]. Adv Geom, 2012, 12(2): 287–301.

    Article  Google Scholar 

  6. Toth G. A measure of symmetry for the moduli of spherical minimal immersions [J]. Geom Dedicata, 2012, 160: 1–14.

    Article  Google Scholar 

  7. Jin H, Guo Q. Asymmetry of convex bodies of constant width [J]. Discrete Comput Geom, 2012, 47: 415–423.

    Article  Google Scholar 

  8. Jin H, Guo Q. A note on the extremal bodies of constant width for the Minkowski measure[J]. Geom Dedicata, 2013, 164: 227–229.

    Article  Google Scholar 

  9. Chakerian G D, Groemer H. Convex bodies of constant width [C]// Convexity and Its Applications. Basel, Boston, Stuttgart: Birkhauser,1983: 49–96.

    Chapter  Google Scholar 

  10. Kawohl B, Weber C. Meissner’s mysterious bodies[J]. Math Intelligencer, 2011, 33(3): 94–101.

    Article  Google Scholar 

  11. Dekster B V. The Borsuk conjecture holds for bodies of revolution [J]. J Geom, 1995, 52(2): 64–73.

    Article  Google Scholar 

  12. Firey W J. Generalized convex bodies of revolution [J]. Canad J Math, 1967, 19: 972–996.

    Article  Google Scholar 

  13. Ryabogin D, Zvavitch A. Reconstruction of convex bodies of revolution from the areas of their shadows[J]. Arch Math, 2004, 83(5): 450–460.

    Article  Google Scholar 

  14. Lachand-Robert T, Oudet E. Bodies of constant width in arbitrary dimension [J]. Math Nachr, 2007, 280(7): 740–750.

    Article  Google Scholar 

  15. Benson R V. Euclidean Geometry and Convexity [M]. New York: McGraw-Hill, 1966.

    Google Scholar 

  16. Besicovitch A S. Measures of asymmetry for convex curves, II. Curves of constant width[J]. J London Math Soc, 1951, 26: 81–93.

    Article  Google Scholar 

  17. Heil E, Martini H. Special convex bodies[C]// Handbook of Convex Geometry. Amsterdam: North-Holland, 1993: 347–385.

    Chapter  Google Scholar 

  18. Schneider R. Convex Bodies: The Brunn-Minkowski Theory [M]. Cambridge: Cambridge University Press, 1993.

    Book  Google Scholar 

  19. Klee V L. The critical set of a convex set [J]. Amer J Math, 1953, 75: 178–188.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Suzhou University of Science and Technology, Suzhou, 215009, Jiangsu, China

    Hailin Jin

Authors
  1. Hailin Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hailin Jin.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (11271244, 11271282)

Biography: JIN Hailin, male, Ph. D., research direction: convex geometric analysis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, H. Asymmetry for convex body of revolution. Wuhan Univ. J. Nat. Sci. 20, 97–100 (2015). https://doi.org/10.1007/s11859-015-1065-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-015-1065-1

Keywords

CLC number

Search

Navigation