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 insp...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.展开更多
Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continui...Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on （1, ＋∞） is confirmed, and the connections between general p-critical points and the Minkowski-critical points （∞-critical points） are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.展开更多
The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-...The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced by Q.Guo.Then,a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R.J.Gardner,D.Hug and W.Weil recently,which is an extension of the p-measures.展开更多
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)
文摘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The NSF(11271282)of Chinathe GIF(CXLX12 0865)of Jiangsu Province
文摘Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on （1, ＋∞） is confirmed, and the connections between general p-critical points and the Minkowski-critical points （∞-critical points） are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271244 and 11271282)
文摘The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced by Q.Guo.Then,a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R.J.Gardner,D.Hug and W.Weil recently,which is an extension of the p-measures.
