论文标题
RICCI范围较低的Kahler歧管的度量刚度和几乎最大的体积
Metric rigidity of Kahler manifolds with lower Ricci bounds and almost maximal volume
论文作者
论文摘要
在此简短说明中，我们证明了具有较低RICCI曲率结合和几乎最大体积的Kahler歧管是Gromov-Hausdorff，靠近带有Fubini-Study Metric的投射空间。这是通过将Kewei Zhang和Yuchen Liu的最新结果结合到此类Kahler歧管的全体形态刚性的最新结果与Tian-Wang的结构定理几乎是爱因斯坦歧管的。这可以被视为在几乎最大体积的riemannian歧管形状上冷水时结果的复杂类似物
In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of Kewei Zhang and Yuchen Liu on holomorphic rigidity of such Kahler manifolds with the structure theorem of Tian-Wang for almost Einstein manifolds. This can be regarded as the complex analog of the result on Colding on the shape of Riemannian manifolds with almost maximal volume
