具有大扭曲的扭曲常数数量曲率Kähler度量的存在性
Existence of twisted constant scalar curvature Kähler metrics with a large twist
摘要：
假设存在两个Kähler度量$ω$和$α$，使得$α$相对于$ω$的度量收缩为常数，即$Λ_ω α= \text{const}$。证明了对所有足够大的$R>0$，在上同调类$[ ω]$中存在一个扭曲的常数数量曲率Kähler度量$ω'$，满足$S(ω' ) - R Λ_{ω' } α= \text{const}$ .我们讨论了它对$K$稳定性和最近由X.X.尘
英文摘要：
Suppose that there exist two Kähler metrics $ω$ and $α$ such that the metric contraction of $α$ with respect to $ω$ is constant, i.e. $Λ_ω α= \text{const}$. We prove that for all large enough $R>0$ there exists a twisted constant scalar curvature Kähler metric $ω'$ in the cohomology class $[ ω]$, satisfying $S(ω' ) - R Λ_{ω' } α= \text{const}$. We discuss its implication to $K$-stability and the continuity method recently proposed by X.X. Chen.
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