The Monge-Ampère operator and geodesics in the space of Kähler potentials
arXiv:math/0504157 · doi:10.1007/s00222-006-0512-1
Abstract
It is shown that geodesics in the space of Kähler potentials can be uniformly approximated by geodesics in the spaces of Bergman metrics. Two important tools in the proof are the Tian-Yau-Zelditch approximation theorem for Kähler potentials and the pluripotential theory of Bedford-Taylor, suitably adapted to Kähler manifolds.
25 pages, no figure, minor misprints corrected