Compactness theorems for gradient Ricci solitons
Compactness theorems for gradient Ricci solitons
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DOI：
10.1016/j.geomphys.2006.01.004
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发表时间：
2005-07
影响因子：
1.5
通讯作者：
Xi Zhang
中科院分区：
文献类型：
--
作者：
Xi Zhang
本文证明了梯度Ricci孤子的紧性定理。设（Mα,gα）为维数n≥4的紧致梯度Ricci孤子序列，其曲率具有一致有界的ln2范数，Ricci曲率自下一致有界，具有一致的下界体积和一致的上界直径；那么必然存在一个子序列（Mα,gα）收敛到一个紧的轨道（M∞,g∞），具有有限多个孤立奇点，其中g∞是轨道意义上的梯度Ricci孤子度规。
In this paper, we prove a compactness theorem for gradient Ricci solitons. Let (Mα,gα) be a sequence of compact gradient Ricci solitons of dimension n≥4, whose curvatures have uniformly bounded Ln2norms, whose Ricci curvatures are uniformly bounded from below, with uniformly lower bounded volume and with uniformly upper bounded diameter; then there must exist a subsequence (Mα,gα) converging to a compact orbifold (M∞,g∞) with finitely many isolated singularities, where g∞is a gradient Ricci soliton metric in an orbifold sense.