We establish the cyclic inequality for i-th L p-dual mixed volume and Lp-dual Urysohn inequality between p-mean width and Lp-dual quermassintegral. Moreover, the dual isoperimetric inequality for Lp-dual mixed volume ...We establish the cyclic inequality for i-th L p-dual mixed volume and Lp-dual Urysohn inequality between p-mean width and Lp-dual quermassintegral. Moreover, the dual isoperimetric inequality for Lp-dual mixed volume is proved, which is an extension of the classical dual isoperimetric inequality.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
In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed inter...In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.展开更多
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
In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, ...In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10971205)
文摘We establish the cyclic inequality for i-th L p-dual mixed volume and Lp-dual Urysohn inequality between p-mean width and Lp-dual quermassintegral. Moreover, the dual isoperimetric inequality for Lp-dual mixed volume is proved, which is an extension of the classical dual isoperimetric inequality.
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.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065)the Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)
文摘In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
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Supported by the National Natural Science Foundation of China(11561020,11161019)
文摘In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.
