In this paper we study the L_(p) dual Minkowski problem for the case p<0<q.We prove for any positive smooth function f on S^(1),there exists an F:R^(+)→R^(-),such that if F(q)<p<0 or 0<q<-F(-p)then ...In this paper we study the L_(p) dual Minkowski problem for the case p<0<q.We prove for any positive smooth function f on S^(1),there exists an F:R^(+)→R^(-),such that if F(q)<p<0 or 0<q<-F(-p)then there is a smooth and strictly convex body solving the planar L_(p) dual Minkowski problem.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11971424 and 11571304)。
文摘In this paper we study the L_(p) dual Minkowski problem for the case p<0<q.We prove for any positive smooth function f on S^(1),there exists an F:R^(+)→R^(-),such that if F(q)<p<0 or 0<q<-F(-p)then there is a smooth and strictly convex body solving the planar L_(p) dual Minkowski problem.
