Interpolation of weighted extremal functions
Peer reviewed, Journal article
Published version
Date
2021-03Metadata
Show full item recordCollections
Original version
Rashkovskii, A. (2021) Interpolation of weighted extremal functions. Arnold Mathematical Journal, 7 (3), 407-417. 10.1007%2Fs40598-021-00175-xAbstract
An approach to interpolation of compact subsets of Cn, including Brunn–Minkowski type inequalities for the capacities of the interpolating sets, was developed in [8] by means of plurisubharmonic geodesics between relative extremal functions of the given sets. Here we show that a much better control can be achieved by means of the geodesics between weighted relative extremal functions. In particular, we establish convexity properties of the capacities that are stronger than those given by the Brunn–Minkowski inequalities.