论文标题
RICCI流量和三维RICCI细节歧管的初始稳定性估计值
Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
论文作者
论文摘要
本文调查了一类RICCI流的稳定性问题，这些流量从可能的非平滑度量空间开始。 We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from below and whose curvature is bounded by $c\cdot t^{-1}$ converge to one another at an exponential rate once they have been appropriately gauged.作为一种应用，我们表明，具有有界曲率的平滑三维，完整的，均匀的ricci-riemannian歧管是紧凑的或平坦的，因此证实了汉密尔顿和洛特的猜想。
This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from below and whose curvature is bounded by $c\cdot t^{-1}$ converge to one another at an exponential rate once they have been appropriately gauged. As an application, we show that smooth three dimensional, complete, uniformly Ricci-pinched Riemannian manifolds with bounded curvature are either compact or flat, thus confirming a conjecture of Hamilton and Lott.
