I-properness of Mabuchi’s K-energy
I-properness of Mabuchi’s K-energy
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万宝至 K 能量的 I 特性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Kai Zheng
中科院分区：
文献类型：
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作者：
Kai Zheng
在Kähler度量空间上，我们首先证明了能量泛函$$\tilde{E}^\beta $$E~β的下界，然后给出了测地线射线检测能量泛函$$\tilde{{\mathfrak {J}}^\beta $$J~β下界的判据.它们被用来获得Mabuchi的K-能量的I-适当性。在一个充分必要条件下，证明了$\tilde{{\mathfrak {J}}^\beta $$J~β-泛函的负梯度流的收敛性.
Over the space of Kähler metrics associated to a fixed Kähler class, we first prove the lower bound of the energy functional $$\tilde{E}^\beta $$E~β, then we provide the criteria of the geodesics rays to detect the lower bound of $$\tilde{{\mathfrak {J}}}^\beta $$J~β-functional . They are used to obtain the I-properness of Mabuchi’s K-energy. The criteria are examined under a necessary and sufficient condition by showing the convergence of the negative gradient flow of $$\tilde{{\mathfrak {J}}}^\beta $$J~β-functional.