Some applications of projective logarithmic potentials

Abstract

In this note, we give some applications of projective logarithmic potentials. First we introduce the notions of projective logarithmic energy and capacity associated to projective kernel. We compare quantitatively the projective logarithmic capacity with the complex Monge-Ampère capacity on complex projective space and we deduce that the set of zero logarithmic capacity is of Monge-Ampère capacity zero. Further, we define transfinite diameter of a compact set and we show that it coincides with logarithmic capacity. Finally we deduce that there is an analogous of classical Evans's theorem.