On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi
1999 Annales Polonici Mathematici  
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings. As a function of the N × n complex variables z ij , VDM is a polynomial of 1991 Mathematics Subject Classification: 32F05, 32E30, 41A10, 31C15.
doi:10.4064/ap-72-3-285-305 fatcat:tlc5hjeanfc55ecxg3dlkvjlki