摘要
Recently, the connection between p-measures of asymmetry and the L_p-mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p-measures of asymmetry for star bodies（naturally for convex bodies） is introduced first. Then the connection between dual p-measures of asymmetry and Lp-dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.
Recently, the connection between p-measures of asymmetry and the L_p-mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p-measures of asymmetry for star bodies（naturally for convex bodies） is introduced first. Then the connection between dual p-measures of asymmetry and Lp-dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.
基金
Supported by the National Natural Science Foundation of China(12671293,11701118,U1201252)
the National High Technology Research&Development Program of China(2015AA015408)
the Special Fund for Science & Technology Platform and Talent Team Project of Guizhou Province(Qian KeHe Ping Tai RenCai [2016]5609)
