The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symm...The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.展开更多
Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curva...Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.展开更多
In this paper, we establish two Dresher's type inequalities for dual quermassintegral with Lp-radial Minkowski linear combination and Lp-harmonic Blaschke linear combination, respectively. Our results in special c...In this paper, we establish two Dresher's type inequalities for dual quermassintegral with Lp-radial Minkowski linear combination and Lp-harmonic Blaschke linear combination, respectively. Our results in special cases yield some new dual Lp-Brunn-Minkowski inequalities for dual quermassintegral.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
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
文摘The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.
基金Supported by the National Natural Science Foundation of China(11161019)
文摘Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.
基金Supported by the National Natural Science Foundation of China（11371224） Supported by the Master Thesis Foundation of China Three Gorges University（2013PY069）
文摘In this paper, we establish two Dresher's type inequalities for dual quermassintegral with Lp-radial Minkowski linear combination and Lp-harmonic Blaschke linear combination, respectively. Our results in special cases yield some new dual Lp-Brunn-Minkowski inequalities for dual quermassintegral.
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)
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.
