发表机构
Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对非负截面曲率的完备非紧流形，建立了数量曲率积分的尖锐渐近界及刚性分类，并推广到闭流形情形。
AI 中文摘要
对于任意完备非紧流形$(M^n, g)$，若其截面曲率非负，且$3\le n\le6$，我们得到$\displaystyle \lim_{r\to\infty}r^{2-n}\int_{B_p(r)}\Sc_g\\,dV_g\le8\pi\omega_{n-2}(1-\AVR(M^n,g))$及相应的刚性。后者界及其等号分类在具有正维数灵魂的$(M^n, g)$中成立。在存在极点的情况下，$\displaystyle \lim_{r\to\infty}r^{2-n}\int_{B_p(r)}\Sc_g\\,dV_g\le4\pi\omega_{n-2}(1-\AVR(M^n,g))$由独立的距离球面证明得出。我们还证明了闭流形上尖锐的总数量积分界，其c
英文摘要
For any complete noncompact manifolds $(M^n, g)$ of nonnegative sectional curvature, with $3\le n\le6$, we obtain $\displaystyle \lim_{r\to\infty}r^{2-n}\int_{B_p(r)}\Sc_g\,dV_g\le8πω_{n-2}(1-\AVR(M^n,g))$ and the corresponding rigidity. The latter bound and its equality classification hold in $(M^n, g)$ with positive-dimensional souls. With a pole, $\displaystyle \lim_{r\to\infty}r^{2-n}\int_{B_p(r)}\Sc_g\,dV_g\le4πω_{n-2}(1-\AVR(M^n,g))$ follows from an independent distance-sphere proof. We also prove the sharp total scalar-integral bound for closed manifolds whose c
