A conformally invariant gap theorem characterizing $$\mathbb {CP}^2$$ via the Ricci flow
A conformally invariant gap theorem characterizing $$\mathbb {CP}^2$$ via the Ricci flow
复制标题
通过 Ricci 流表征 $$mathbb {CP}^2$$ 的共形不变间隙定理
DOI：
10.1007/s00209-019-02331-8
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发表时间：
2020
影响因子：
0.8
通讯作者：
Zhang, Siyi
中科院分区：
文献类型：
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作者：
Chang, Sun-Yung A.;Gursky, Matthew;Zhang, Siyi
推广了Chang等人的球面定理。(Publ Math Inst Htétude Sci 98：105-434,2003)给出了的共形不变刻画。特别地，我们引入了一个定义在满足‘正性’条件的共形四维流形上的共形不变量，它是由Chang等人提出的。(2003)，如果，则是微分同胚于。本文的主要结果是一个‘间隙’结果，表明如果足够小，则微分同胚于。Ricci流被用于从边界传递到逐点曲率信息的关键方式。
We extend the sphere theorem of Chang et al. (Publ Math Inst Ht Études Sci 98:105–434, 2003) to give a conformally invariant characterization of. In particular, we introduce a conformal invariantdefined on conformal four-manifolds satisfying a ‘positivity’ condition; it follows from Chang et al. (2003) that if, thenis diffeomorphic to. Our main result of this paper is a ‘gap’ result showing that ifandforsmall enough, thenis diffeomorphic to. The Ricci flow is used in a crucial way to pass from the bounds onto pointwise curvature information.