The Orlicz Minkowski problem for logarithmic capacity seeks to determine the necessary and sufficient conditions for a given finite Borel measure,such that it is the Orlicz logarithmic capacitary measure of a convex b...The Orlicz Minkowski problem for logarithmic capacity seeks to determine the necessary and sufficient conditions for a given finite Borel measure,such that it is the Orlicz logarithmic capacitary measure of a convex body.The Orlicz Minkowski problem for loga-rithmic capacity includes the Minkowski problem for logarithmic capacity and the Lp Minkowski problem for logarithmic capacity as special cases.The discrete case has been solved by the researchers.In this paper,we solve the Orlicz Minkowski problem for logarithmic capacity with respect to general Borel measures by applying an approximation scheme.展开更多
In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvatu...In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.展开更多
In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total vari...In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.展开更多
A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with i...A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.展开更多
Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang(Communications on Pure and Applied Mathematics,2024),which is an extension of the surface are...Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang(Communications on Pure and Applied Mathematics,2024),which is an extension of the surface area measure.The Minkowski problems for chord measures was considered by Lutwak-Xi-Yang-Zhang.In this paper,we use variational method to solve the even Orlicz chord Minkowski problem.The obtained results are an extension of the even Orlicz Minkowski problem from Haberl-Lutwak-Yang-Zhang(Advances in Mathematics,2010).展开更多
In this paper,we introduce the normalized L,mixed intersection body and demonstrate how the normalized L_(p) mixed intersection body operator can be used to obtain the polar body operator as a limit.Moreover,we study ...In this paper,we introduce the normalized L,mixed intersection body and demonstrate how the normalized L_(p) mixed intersection body operator can be used to obtain the polar body operator as a limit.Moreover,we study the L_(p)-Busemann-Petty type problem for the normalized L_(p) mixed intersection bodies.展开更多
基金Supported by Postgraduate Scientific Research Innovation Project of Hunan Province(CX20231033)Science and Technology Research Project of Jiangxi Provincial Education Department(GJJ210815)+2 种基金Jiangxi Provincial Natural Science Foundation(20232BAB201005)the National Natural Science Founda-tion of China(12461010,12161043)the Scientific Research Fund of Hunan Provincial Education Department(24A0338)。
文摘The Orlicz Minkowski problem for logarithmic capacity seeks to determine the necessary and sufficient conditions for a given finite Borel measure,such that it is the Orlicz logarithmic capacitary measure of a convex body.The Orlicz Minkowski problem for loga-rithmic capacity includes the Minkowski problem for logarithmic capacity and the Lp Minkowski problem for logarithmic capacity as special cases.The discrete case has been solved by the researchers.In this paper,we solve the Orlicz Minkowski problem for logarithmic capacity with respect to general Borel measures by applying an approximation scheme.
基金supported by the National Natural Science Foundation of China(12171144,12231006,12122106).
文摘In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.
基金Supported in part by NSFC(No.11971005)the Fundamental Research Funds for the Central Universities(Nos.GK202101008,GK202102012)。
文摘In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.
文摘A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.
基金Supported by the National Natural Science Foundation of China(12071277,12071334)。
文摘Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang(Communications on Pure and Applied Mathematics,2024),which is an extension of the surface area measure.The Minkowski problems for chord measures was considered by Lutwak-Xi-Yang-Zhang.In this paper,we use variational method to solve the even Orlicz chord Minkowski problem.The obtained results are an extension of the even Orlicz Minkowski problem from Haberl-Lutwak-Yang-Zhang(Advances in Mathematics,2010).
基金Supported by the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20231033)。
文摘In this paper,we introduce the normalized L,mixed intersection body and demonstrate how the normalized L_(p) mixed intersection body operator can be used to obtain the polar body operator as a limit.Moreover,we study the L_(p)-Busemann-Petty type problem for the normalized L_(p) mixed intersection bodies.
