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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, we prove that if K is a convex body in $E^n$ and $E_i$ and $E_o$ are inscribed ellipsoid and circumscribed ellipsoid of K respectively with ${\alpha}E_i=E_o$, then $\[({\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n{\geq}V(K)V({\Gamma}^{\ast}_pK){\geq}\[(\frac{1}{\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n$. Lutwak and Zhang[6] proved that if K is a convex body, ${\omega}^2_n=V(K)V({\Gamma}_pK)$ if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.
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참고문헌 (8)
참고문헌 신청
G. D. Chakerian / 1983 / Convex Bodies of Constant Width, In: Convexity and Its Applications / Birkhauser
H.G. Eggleston / 1958 / Convexity / Cambridge Univ. Press
R. J. Gardner / 1995 / Geometric Tomography / Cambridge Univ. Press
H. Groemer / 1988 / Stability Theorem for convex domains of constant width / Canad. Math. Bull 31:328~337
R. Howard / 2006 / Convex bodies of constant width and constant brightness / Adv. Math 204(1):241~261
H.G. Eggleston / 1958 / Convexity / Cambridge Univ. Press
R. J. Gardner / 1995 / Geometric Tomography / Cambridge Univ. Press
H. Groemer / 1988 / Stability Theorem for convex domains of constant width / Canad. Math. Bull 31:328~337
R. Howard / 2006 / Convex bodies of constant width and constant brightness / Adv. Math 204(1):241~261
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