Theory of surround system and associated inequalities

In this paper, we define the surround system S(m){Γ,l}S(m){Γ,l} and the surround system with a center S(2){P,Γ,l}S(2){P,Γ,l}. Under the proper hypotheses, we establish several geometric inequalities for S(2){P,Γ,l}S(2){P,Γ,l}. As applications, we give the background of the surround system with a center S(2){P,Γ,l}S(2){P,Γ,l} in space science.