Title: Sharpening a gap theorem: nonnegative Ricci and small curvature concentration Show Chinese title

Title: 加强一个间隙定理：非负 Ricci 曲率和小曲率集中

Abstract: We sharpen a gap theorem of Chan & Lee for nonnegative Ricci curvature manifolds that have positive asymptotic volume ratio and small enough scale-invariant integral curvature (so-called "curvature concentration"), by showing that the curvature concentration need only depend linearly on the asymptotic volume ratio. We prove the result by exhibiting a long-time Ricci flow solution with faster than $1/t$ curvature decay, which allows us to shift the limiting contradiction argument to time infinity and thus obtain an explicit bound on the size of the gap. Show Chinese abstract

Abstract: 我们通过证明曲率集中只需与渐近体积比线性相关，从而改进了Chan & Lee关于具有正渐近体积比和足够小的尺度不变积分曲率（所谓的“曲率集中”）的非负Ricci曲率流形的间隙定理。 我们通过展示一个长时间Ricci流解，其曲率衰减快于$1/t$，从而将极限矛盾论证转移到时间无穷远，因此得到间隙大小的显式界。