论文标题
Kahler-Einstein指标和特征值差距
Kahler-Einstein Metrics and Eigenvalue Gaps
论文作者
论文摘要
Kahler-Einstein指标在FANO歧管上的存在的特征是在平滑矢量场上0和Cauchy-Riemann操作员的第一个正征值之间的均匀差距和第一个正征值。它的特征在于，汉密尔顿载体场的0和第一个正征值之间的差距类似。基础工具是针对卡勒电位空间适当界限子集的紧凑标准，这意味着正差距。
The existence of Kahler-Einstein metrics on a Fano manifold is characterized in terms of a uniform gap between 0 and the first positive eigenvalue of the Cauchy-Riemann operator on smooth vector fields. It is also characterized by a similar gap between 0 and the first positive eigenvalue for Hamiltonian vector fields. The underlying tool is a compactness criterion for suitably bounded subsets of the space of Kahler potentials which implies a positive gap.
