Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

INEQUALITIES FOR THE AREA OF CONSTANT RELATIVE BREADTH CURVES

  • Kim, Yong-Il (Department of Mathematics, Sungkyunkwan University) ;
  • Chai, Y.D. (Department of Mathematics, Sungkyunkwan University)
  • Published : 1999.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain an efficient upper bound of the area of convex curves of constant relative breadth in the Minkowski plane. The estimation is given in terms of the Minkowski are length of pedal curve of original curve.

Keywords

References

  1. Proc. Sympos. Pure Math. v.Ⅶ Minimum area of a set of constant width A. S. Besicovitch
  2. D. Dissertation, Oklahoma State University Characterizations and properties of sets of constant width M. M. Bontrager
  3. American Journal of Mathematics v.69 The isoperimetric problem in the Minkowski plane H. Busemann
  4. The Youngnam Mathematical Journal v.1 Geometric inequalities in Minkowski plane Y. D. Chai;Y. I. Kim
  5. Comm. Korean Math. Soc. v.12 no.3 An estimate of the area of constant breadth curves Y. D. Chai;Y. I. Kim
  6. Kyungpook Math. J. v.37 no.2 Constant breadth curves in the Minkowski plane Y. D. Chai;Y. I. Kim
  7. Pacific J. Math. v.19 Sets of constant width G. D. Chakerian
  8. Duke Math. J. v.29 Integral geometry in the Minkowski plane G. D. Chakerian
  9. Trans. Amer. Math. Soc. v.129 Sets of constant relative width and constant relative brightness G. D. Chakerian
  10. Convexity and its applications Convex bodies of constant width G. D. Chakerian;H. Groemer;P. M. Gruber(ed.);J. M. Wills(ed.)
  11. Israel J. Math. v.3 Sets of constant width in finite dimensional Banach spaces H. G. Eggleston
  12. Handbook of convex geometry P. M. Gruber;J M. Wills
  13. Amer. Math. Monthly v.64 Curves with a kind of constant width P. J. Kelly
  14. Honam Math. J. v.19 no.1 Geometric properties of curves in the Minkowski plane Y. I. Kim;Y. D. Chai
  15. Integral geometry and geometric probability L. A. Santalo
  16. Math. Practice and Theory v.1 On the inverse of Holder's inequality L. Xiao-hua