标题： 4-流形上正Yamabe不变量的Weyl泛函 显示英文标题

标题： The Weyl functional on 4-manifolds of positive Yamabe invariant

摘要： 表明在每个具有正标量曲率的闭合定向黎曼4-流形$(M,g)$上，$$\int_M|W^+_g|^2d\mu_{g}\geq 2\pi^2(2\chi(M)+3\tau(M))-\frac{8\pi^2}{|\pi_1(M)|},$$其中$W^+_g$、$\chi(M)$和$\tau(M)$分别表示$g$的自对偶 Weyl 张量、$M$的欧拉示性数和符号。 这推广了Gursky的不等式\cite{gur}对于$b_1(M)>0$的情况，方式要简单得多。 我们还将所有此类Weyl泛函的下界扩展到4轨道流形，包括Gursky对于$b_2^+(M)>0$或$\delta_gW^+_g=0$的情况，并获得了自对偶轨道流形度量存在性的拓扑障碍。 显示英文摘要

摘要： It is shown that on every closed oriented Riemannian 4-manifold $(M,g)$ with positive scalar curvature, $$\int_M|W^+_g|^2d\mu_{g}\geq 2\pi^2(2\chi(M)+3\tau(M))-\frac{8\pi^2}{|\pi_1(M)|},$$ where $W^+_g$, $\chi(M)$ and $\tau(M)$ respectively denote the self-dual Weyl tensor of $g$, the Euler characteristic and the signature of $M$. This generalizes Gursky's inequality \cite{gur} for the case of $b_1(M)>0$ in a much simpler way. We also extend all such lower bounds of the Weyl functional to 4-orbifolds including Gursky's inequalities for the case of $b_2^+(M)>0$ or $\delta_gW^+_g=0$, and obtain topological obstructions to the existence of self-dual orbifold metrics of positive scalar curvature.