The Monge-Amp\`ere operator and geodesics in the space of K\"ahler potentials
Differential Geometry
2009-11-11 v2 Complex Variables
Abstract
It is shown that geodesics in the space of K\"ahler 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 K\"ahler potentials and the pluripotential theory of Bedford-Taylor, suitably adapted to K\"ahler manifolds.
Cite
@article{arxiv.math/0504157,
title = {The Monge-Amp\`ere operator and geodesics in the space of K\"ahler potentials},
author = {D. H. Phong and Jacob Sturm},
journal= {arXiv preprint arXiv:math/0504157},
year = {2009}
}
Comments
25 pages, no figure, minor misprints corrected