Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
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发表时间：
2022-03
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通讯作者：
Alix Deruelle;F. Schulze;Miles Simon
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作者：
Alix Deruelle;F. Schulze;Miles Simon
.本文研究了一类从可能非光滑度量空间出发的Ricci流形的稳定性问题。我们证明了，如果初始度量空间是Reifenberg和局部双Lipschitz到欧氏空间，则Ricci曲率从下到上一致有界且曲率由c · t − 1有界的Ricci算子的两个解一旦被适当地度量就以指数速度收敛到另一个解。作为应用，我们证明了具有有界曲率的光滑三维完备一致Ricci-pinched黎曼流形是紧的或非紧的，从而证实了汉密尔顿和Lott的一个猜想.
. 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 · 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.