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
In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fu...In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.展开更多
Lutwak showed the radial bodies combining with the radial Minkowski linear combinations of star bodies. In this paper, the general radial bodies are introduced and its some properties and inequalities are established.
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
The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bod...The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.展开更多
According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequali...According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.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.
文摘In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.
基金Supported by the National Natural Science Foundation of China（11371224） Supported by the Academic Mainstay Foundation of Hubei Pnvince（B2016030）
文摘Lutwak showed the radial bodies combining with the radial Minkowski linear combinations of star bodies. In this paper, the general radial bodies are introduced and its some properties and inequalities are established.
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.
文摘The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.
基金Supported by the National Natural Science Foundation of China(11161019,11561020)the Science and Technology Plan of Gansu Province(145RJZG227)
文摘According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.
