In this paper,we introduce the concept of the L_(p,s)-Gaussian surface area measure of a convex body in n-dimensional Euclidean space R^(n) and formulate the corresponding L_(p,s)-Gaussian-Minkowski problem:Given a fi...In this paper,we introduce the concept of the L_(p,s)-Gaussian surface area measure of a convex body in n-dimensional Euclidean space R^(n) and formulate the corresponding L_(p,s)-Gaussian-Minkowski problem:Given a finite Borel measureμon S^(n-1),what are the necessary and sufficient conditions for the existence of a convex body whose L_(p,s)-Gaussian surface area measure equals measure μ?Furthermore,we present a solution to the L_(p,s)-Gaussian-Minkowski problem for the case of even measures.展开更多
基金Supported by the National Natural Science Foundation of China(11971080,12371137)。
文摘In this paper,we introduce the concept of the L_(p,s)-Gaussian surface area measure of a convex body in n-dimensional Euclidean space R^(n) and formulate the corresponding L_(p,s)-Gaussian-Minkowski problem:Given a finite Borel measureμon S^(n-1),what are the necessary and sufficient conditions for the existence of a convex body whose L_(p,s)-Gaussian surface area measure equals measure μ?Furthermore,we present a solution to the L_(p,s)-Gaussian-Minkowski problem for the case of even measures.
