In this article, some dual Brunn-Minkowski inequalities are established for star dual of mixed intersection bodies with respect to the harmonic p-combination and p-radial linear combination.
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 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, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the. d...In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the. dual Brunn-Minkowski inequalities) are established for mixed intersection bodies.展开更多
If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding ...If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn（K）≤μn（L）. This extends a generalized Funk＇s section theorem for volumes to that for measures.展开更多
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
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
In this paper, we introduce the concept of dual quermassintegral differences. Further, we give the dual Brunn-Minkowski inequality and dual Minkowski inequality for dual quermassintegral differences for mixed intersec...In this paper, we introduce the concept of dual quermassintegral differences. Further, we give the dual Brunn-Minkowski inequality and dual Minkowski inequality for dual quermassintegral differences for mixed intersection bodies.展开更多
This paper presents modified version of an affirmative answer of Centro symmetric convex body Busemann-Petty problem, and proved that at all strings about the origin, the star dual of ball has the smallest volume.
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
基金Supported by the National Natural Sciences Foundation of China (10801140)
文摘In this article, some dual Brunn-Minkowski inequalities are established for star dual of mixed intersection bodies with respect to the harmonic p-combination and p-radial linear combination.
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 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Project supported by the National Natural Science Foundation of China (No.10271071).
文摘In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the. dual Brunn-Minkowski inequalities) are established for mixed intersection bodies.
基金Supported by the National Natural Science Foundation of China(10801140)Chongqing Research Program of Basic Research and Frontier Technology(2013-JCYJ-A00005)the Foundation of Chongqing Normal University(13XLZ05)
文摘If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn（K）≤μn（L）. This extends a generalized Funk＇s section theorem for volumes to that for measures.
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 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.
文摘In this paper, we introduce the concept of dual quermassintegral differences. Further, we give the dual Brunn-Minkowski inequality and dual Minkowski inequality for dual quermassintegral differences for mixed intersection bodies.
文摘This paper presents modified version of an affirmative answer of Centro symmetric convex body Busemann-Petty problem, and proved that at all strings about the origin, the star dual of ball has the smallest volume.
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.
