Uniform K-stability and asymptotics of energy functionals in Kähler geometry
Uniform K-stability and asymptotics of energy functionals in Kähler geometry
复制标题
DOI：
10.4171/jems/894
复制
发表时间：
2016-03
影响因子：
2.6
通讯作者：
S. Boucksom;Tomoyuki Hisamoto;Mattias Jonsson
中科院分区：
文献类型：
--
作者：
S. Boucksom;Tomoyuki Hisamoto;Mattias Jonsson
考虑一个极化复流形（X，L）和L上的一条由（X，L）的测试配置上的正度量定义的正度量射线。对于K\"ahler几何中的大多数常见泛函，我们证明了在无穷远处沿着射线的斜率是通过在由测试配置定义的L上的非阿基米德度量处评估泛函的非阿基米德版本（如我们先前的论文中定义的）来给出的。利用这一渐近结果，我们证明了Mabuchi泛函的非线性蕴含一致K-稳定性。作为一个部分的逆，我们表明，一致的K-稳定性意味着的马渊功能时，限制伯格曼度量的不确定性。
Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in K\"ahler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability. As a partial converse, we show that uniform K-stability implies coercivity of the Mabuchi functional when restricted to Bergman metrics.