Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In ...Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.展开更多
Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a...Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.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
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
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
In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski...In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski type inequalities of general Lp-intersection bodies for dual quermassintegrals, respectively. As applications, inequalities of volume are derived.展开更多
Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassi...Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassintegrals are established. As the applications, we obtain the lower bounds of dual quermassintegrals product. Further, the Brunn-Minkowski type inequality and the cycle inequality for the Lp-dual mixed quermassintegrals are given.展开更多
基金Supported by the Natural Science Foundation of China(10671117)Supported by the Science Foundation of China Three Gorges University
文摘Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.
文摘Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.
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.
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.
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.
基金the National Natural Science Foundation of China(11371224)the Innovation Foundation of Graduate Student of China Three Gorges University(2019SSPY146)。
文摘In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski type inequalities of general Lp-intersection bodies for dual quermassintegrals, respectively. As applications, inequalities of volume are derived.
基金Supported by the National Natural Science Foundation of China(11371224)
文摘Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassintegrals are established. As the applications, we obtain the lower bounds of dual quermassintegrals product. Further, the Brunn-Minkowski type inequality and the cycle inequality for the Lp-dual mixed quermassintegrals are given.
