In this article,we explain how the famous Archimedes’principle of flotation can be used to construct various floating bodies.We survey some of the most important results regarding the floating bodies,including their ...In this article,we explain how the famous Archimedes’principle of flotation can be used to construct various floating bodies.We survey some of the most important results regarding the floating bodies,including their relations with affine surface area and projection body,their extensions in different settings such as space forms and log-concave functions,and mention some associated open problems.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
Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, t...Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^-u = v.展开更多
Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applyin...Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.展开更多
基金supported by the Research Funding of Wuhan Polytechnic University(2024RZ083)Elisabeth M.Werner’s work was supported by the NSF grant DMS-2103482.Deping Ye’s work was supported by an NSERC grant,Canada.Ning Zhang’s work was supported by the NSF of China(11901217,11971005).
文摘In this article,we explain how the famous Archimedes’principle of flotation can be used to construct various floating bodies.We survey some of the most important results regarding the floating bodies,including their relations with affine surface area and projection body,their extensions in different settings such as space forms and log-concave functions,and mention some associated open problems.
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.
基金Supported by the National Natural Science Foundation of China(11271359)
文摘Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^-u = v.
基金Supported by National Natural Science Foundation of China(Grant Nos.11161019 and 11371224)the Science and Technology Plan of the Gansu Province(Grant No.145RJZG227)
文摘Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.
