Prescribed L_p quotient curvature problem and related eigenvalue problem

In this paper, we investigate the existence of admissible (and strictly convex) smooth solutions to the prescribed L_p quotient type curvature problem with p>1. For cases where p=k-l+1 and p> k-l+1, we obtain an admissible solution without any additional conditions, which is strictly spherically convex under a convexity condition. Under the same convexity condition, we establish the existence of a strictly spherically convex solution for the case p更多