The Monge-Ampère operator and geodesics in the space of Kähler potentials

Details The Monge-Ampère operator and geodesics in the space of Kähler potentials The Monge-Ampère operator and geodesics in the space of Kähler potentials

2005-04-07

arxiv.org/abs/math/0504157v2

Mathematics

Differential Geometry

25 pages, no figure, minor misprints corrected

Scientific paper

10.1007/s00222-006-0512-1

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.

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