In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp ...In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.展开更多
In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, ...In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from L_p-counterparts is established.展开更多
Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore,...Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.展开更多
Haberl and Ludwig introduced the L_p-intersection body I_pK for an originsymmetric star body K in R^n,where p < 1 and p ≠ 0.In this paper,we consider the Busemann-Petty's problem for L_p-intersection bodies I_...Haberl and Ludwig introduced the L_p-intersection body I_pK for an originsymmetric star body K in R^n,where p < 1 and p ≠ 0.In this paper,we consider the Busemann-Petty's problem for L_p-intersection bodies I_pK and I_pL.That is,whether I_pK ■ IpL implies Vol_n(K) ≤ Vol_n(L).We obtain that for two origin-symmetric star bodies K and L in R^n,such that(R^n,||·||K) embeds in L_p and I_pK ■ IpL,then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0.展开更多
In this paper, by using the Brunn-Minkowskio-Firey mixed volume theory and dual mixed volume theory, associated with Lp intersection body and dual mixed volume, some dual Brunn-Minkowski inequalities and their isolate...In this paper, by using the Brunn-Minkowskio-Firey mixed volume theory and dual mixed volume theory, associated with Lp intersection body and dual mixed volume, some dual Brunn-Minkowski inequalities and their isolate forms are established for Lp intersection body about the normalized Lp radial addition and Lp radial linear combination. Some properties of operator Lp are given.展开更多
Recently, the notion of general （containing symmetric and asymmetric） Lp-intersection bodies was given. In this article, by the Lp-dual mixed volumes and the general Lp-dual Blaschke bodies, we study the Lp-dual aff...Recently, the notion of general （containing symmetric and asymmetric） Lp-intersection bodies was given. In this article, by the Lp-dual mixed volumes and the general Lp-dual Blaschke bodies, we study the Lp-dual affine surface area forms of the Busemann-Petty problems for general Lp-intersection bodies. Our works belong to a new and rapidly evolving asymmetric Lp-Brtmn-Minkowski theory.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
For 0 〈 p 〈 1, Haberl and Ludwig defined the notions of symmetric Lp-intersection body and nonsymmetric Lp-intersection body. In this paper, we introduce the general Lp-intersection bodies. Furthermore, the Busemann...For 0 〈 p 〈 1, Haberl and Ludwig defined the notions of symmetric Lp-intersection body and nonsymmetric Lp-intersection body. In this paper, we introduce the general Lp-intersection bodies. Furthermore, the Busemann-Petty problems for the general Lp-intersection bodies are shown.展开更多
The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the ...The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.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
基金Project supported by the National Natural Science Foundation of China (Grant No.10671119)the Shanghai Leading Academic Discipline Project (Grant No.J50101)the Shanghai University Graduate Innovation Foundation Project (GrantNo.SHUCX092003)
文摘In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.
基金Supported by the National Natural Science Foundation of China（11561020, 11371224）
文摘In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from L_p-counterparts is established.
基金Supported by the Natural Science Foundation of Hunan Province（2017JJ3085＋16C0635） Supported by the China Postdoctoral Science Foundation（2016M601644）
文摘Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.
基金Supported by the NNSF of China(11161019)Supported by the Foundation of the Education Department of Gansu Province(1009B-09)
文摘Haberl and Ludwig introduced the L_p-intersection body I_pK for an originsymmetric star body K in R^n,where p < 1 and p ≠ 0.In this paper,we consider the Busemann-Petty's problem for L_p-intersection bodies I_pK and I_pL.That is,whether I_pK ■ IpL implies Vol_n(K) ≤ Vol_n(L).We obtain that for two origin-symmetric star bodies K and L in R^n,such that(R^n,||·||K) embeds in L_p and I_pK ■ IpL,then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0.
基金the National Natural Science Foundation of China(No.10671117).
文摘In this paper, by using the Brunn-Minkowskio-Firey mixed volume theory and dual mixed volume theory, associated with Lp intersection body and dual mixed volume, some dual Brunn-Minkowski inequalities and their isolate forms are established for Lp intersection body about the normalized Lp radial addition and Lp radial linear combination. Some properties of operator Lp are given.
基金Supported by the National Natural Science Foundation of China(11371224)
文摘Recently, the notion of general （containing symmetric and asymmetric） Lp-intersection bodies was given. In this article, by the Lp-dual mixed volumes and the general Lp-dual Blaschke bodies, we study the Lp-dual affine surface area forms of the Busemann-Petty problems for general Lp-intersection bodies. Our works belong to a new and rapidly evolving asymmetric Lp-Brtmn-Minkowski theory.
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.
基金Supported by National Natural Science Foundation of China(Grant No.11371224)Foundation of Degree Dissertation of Master of China Three Gorges University(Grant No.2014PY067)
文摘For 0 〈 p 〈 1, Haberl and Ludwig defined the notions of symmetric Lp-intersection body and nonsymmetric Lp-intersection body. In this paper, we introduce the general Lp-intersection bodies. Furthermore, the Busemann-Petty problems for the general Lp-intersection bodies are shown.
基金Supported by National Natural Sciences Foundation of China(10671117)
文摘The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.
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Project supported by the National Natural Science Foundation of China(11561020,11371224,11161019)the Science and Technology Plan of Gansu Province of China(145RJZG227)
