The Monge-Ampère operator and geodesics in the space of Kähler potentials
The Monge-Ampère operator and geodesics in the space of Kähler potentials
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DOI：
10.1007/s00222-006-0512-1
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发表时间：
2005-04
影响因子：
3.1
通讯作者：
D. Phong;J. Sturm
中科院分区：
文献类型：
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作者：
D. Phong;J. Sturm
证明了K“ahler势空间中的测地线可以用Bergman度量空间中的测地线一致逼近.证明中的两个重要工具是K\“ahler势的Tian-Yau-Zelditch逼近定理和适用于K\“ahler流形的Bedford-Taylor多势理论。
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.