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We give some criteria for a-minimally thin sets and a-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 an a-rarefied set. Finally we illustrate the relation between the a-minimally thin set and the a-rarefied set in a cone. © 2012 Pinhong Long et al.

Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone