We give some criteria fora-minimally thin sets anda-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or ∞ with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside ana-rarefied set. Finally we illustrate the relation between thea-minimally thin set and thea-rarefied set in a cone.
AbstractThis paper shows that some characterizations of minimally thin sets connected with a domain having smooth boundary and a half-space in particular also hold for the minimally thin sets at a corner point of a special domain with corners, i.e., the minimally thin set at ∞ of a cone.
Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone