대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제38권4호
  • /
  • Pages.735-740
  • /
  • 2001
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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VOLUME PRODUCT FOR PEDAL BODIES

  • Chai, Y.D. (DEPARTMENT OF MATHEMATICS, SUNGKYUNKWAN UNIVERSITY) ;
  • Kim, Yong-Il (DEPARTMENT OF MATHEMATICS, SUNGKYUNKWAN UNIVERSITY) ;
  • Lee, Doo-Hann (DEPARTMENT OF MATHEMATICS, SUNGKYUNKWAN UNIVERSITY)
  • 발행 : 2001.01.01
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초록

Let K be a convex body of constant relative breadth and let $K^*$ be its polar dual with respect to the Euclidean unit circle. In this paper we obtain the lower bound for the volume of the pedal body $PK^*P $K^{*}$ of K^*.$ Using this, we also obtain the lower bound for the volume product V$(PK^*)$V(PK) for planar bodies.s.

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참고문헌

  1. Ber. Verh. Sa chs. Akad. Wiss. Leipzig Math-Naturw. KI v.68 Raumliche Variationsprobleme mit symmetricher Transversalit-atsbedingung W. Blaschke
  2. Amer. J. Math. v.71 The isoperimetric problem for Minkowski area H. Busemann
  3. Convexity and Its Applications Convex bodies of constant width G. D. Chakerian;Groemer;P. M. Gruber(ed.);J. M. Wills. Birkhauser(ed)
  4. Amer. Math. Monthly v.64 Curves with a kind of constant width P. J. Kelly
  5. Convex Bodies: The Brunn-Minkowski Theory R. Schneider
  6. Minkowski geometry A. C. Thomson