A generalized rotationally symmetric case of the centroaffine Minkowski problem

In this paper the centroaffine Minkowski problem, a critical case of the Lp-Minkowski problem in the n+1 dimensional Euclidean space, is studied. By its variational structure and the method of blow-up analyses, we obtain two sufficient conditions for the existence of solutions, for a generalized rotationally symmetric case of the problem.