Applications of properties of minimally thin sets at infinity with respect tothe Schrödinger operator

Abstract

Let $u$ be a superfunction in a cone. As applications of some criterions and geometrical properties of minimally thin sets at infinity with respect tothe Schrodinger operator, in this paper we prove that the exceptional sets$\{P=(r,\Theta)\in~C_n(\Omega);u(P)>~V(r)\varphi(\Theta)\}$and$\{P=(r,\Theta)\in~C_n(\Omega);u(P)>~V(r)\}$ in a cone are minimally thin set and rarefied set at infinity with respect tothe Schrodinger operator respectively if and only the measures associated with $u$ satisfy certain integral 条件.