Circular cone and its Gauss map

Miekyung Choi; Dong-Soo Kim; Young Ho Kim; Dae Won Yoon

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The $H$ -cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an $H$ -cone. There are given an integral representation theorem and a representation theorem as an $H$ -cone of functions for which fine topology, thinnes, negligible sets and the...