We shall give two criterions of Wiener type which characterize minimally thin sets and rarefied sets in a cone. We shall also show that a positive superharmonic function on a cone behaves regularly outside a rarefied set in a cone. These facts are known for a half space which is a special cone.
"Two criterions of Wiener type for minimally thin sets and rarefied sets in a cone." J. Math. Soc. Japan 54 (3) 487 - 512, July, 2002. https://doi.org/10.2969/jmsj/1191593906