发表机构
University of Notre Dame; Scuola Normale Superiore（圣母大学; 比萨高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明满足特定拓扑条件的正截面曲率闭爱因斯坦四维流形必等距同伦于标准球面或复射影空间，利用共形爆破的ADM质量上下界。
AI 中文摘要
我们证明了满足正截面曲率且欧拉示性数与符号差满足$2\backslash chi(M)-3|\backslash tau(M)|\backslash le4$的闭爱因斯坦四维流形$(M,g)$必与标准球面$S^4$或带有Fubini-Study度量的$\backslash mathbb{CP}^2$等距同伦。证明依赖于$(M,g)$的共形爆破的ADM质量的上界，并结合自\backslash cite{GM}的下界。
英文摘要
We prove that closed Einstein four-manifolds $(M,g)$ with positive sectional curvature and Euler characteristic and signature satisfying $2χ(M)-3|τ(M)|\le4$ must be homothetically isometric to the round $S^4$ or to $\mathbb{CP}^2$ with the Fubini-Study metric. The proof relies on an upper bound on the ADM mass of conformal blow-ups of $(M,g)$, combined with a lower one from \cite{GM}.
Comments9 pages
