紧凑 K"ahler 流形上退化复 Monge-Ampère 方程
微分几何
2009-03-24 v3
摘要
我们证明了某些非常一般类型的退化复 Monge-Ampère 方程在紧凑 K"ahler 流形上的解的存在性和唯一性。这种类型的方程正是用于在不可约奇异 K"ahler 空间上构造 K"ahler-Einstein 度量以及在一般类型的 variety 上构造奇异 K"ahler-Einstein 度量所必需的。
引用
@article{arxiv.0710.5109,
title = {Degenerate complex Monge-Amp\`ere equations over compact K\"ahler manifolds},
author = {Jean-Pierre Demailly and Nefton Pali},
journal= {arXiv preprint arXiv:0710.5109},
year = {2009}
}
备注
The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, which had to be shortened in view of the length of the manuscript and of the demands of referees - in particular it gives more details about the relation with the existing litterature (see Appendix C)