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논문KCI 등재

MIXED CHORD-INTEGRALS OF STAR BODIES

Department of Mathematics
대한수학회 (The Korean Mathematical Society)|2010.03|대한수학회지 (Journal of the KMS)|제47권 제2호|pp. 277-288

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참고문헌

키워드

Fenchel-Aleksandrov inequalitymixed intersection bodiesmixed chord-integralsBieberbach inequality
주제분류수학

초록

The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.

Abstract

The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.

참고문헌 (16)

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  10. E. Lutwak, "Mixed projection inequalities", Trans. Amer. Math. Soc., 287(1), pp.91~105 (1985)
  11. E. Lutwak, "Intersection bodies and dual mixed volumes", Adv. in Math., 71(2), pp.232~261 (1988)
  12. E. Lutwak, "Inequalities for mixed projection bodies", Trans. Amer. Math. Soc., 339(2), pp.901~916 (1993)
  13. L. Santal´o, "An affine invariant for convex bodies of n-dimensional space", Portugaliae Math., 8, pp.155~161 (1949)
  14. R. Schneider, "Convex Body: The Brunn-Minkowski Theory" (1993), Cambridge Univ. Press
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  16. C. J. Zhao, "On polars of mixed projection bodies", J. Math. Anal. Appl., 316(2), pp.664~678 (2006)

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