Some applications of Projective Logarithmic Potentials
Abstract
We continue the study in As18, AAZ18 by giving a multitude of applications of projective logarithmic potentials. First we introduce the notions of projective logarithmic energy and capacity associated to projective kernel that was introduced and studied in As18, AAZ18. We compare quantitatively the projective logarithmic capacity with the complex Monge-Amp\`ere capacity on Pn and we deduce that the set of zero logarithmic capacity is of Monge-Amp\`ere 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 that for any compact set K of zero projective logarithmic capacity shows the existence of Probability measure whose potential admits K as polar set.