Bubble-tree convergence and local diffeomorphism finiteness for gradient Ricci shrinkers
Bubble-tree convergence and local diffeomorphism finiteness for gradient Ricci shrinkers
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DOI：
10.1007/s00209-023-03272-z
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发表时间：
2022-06
影响因子：
0.8
通讯作者：
R. Buzano;Louis Yudowitz
中科院分区：
文献类型：
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作者：
R. Buzano;Louis Yudowitz
我们证明了具有一致有界熵和一致局部能量界的梯度Ricci收缩器序列的泡树收敛，改进了Haslhofer和Müller的紧致性理论（Geom Funct Anal 21：1091-1116，2011; Proc Am Math Soc 143（10）：4433-4437，2015）。特别是，我们表明，没有能量集中在颈部区域，这意味着一个本地的能量身份的序列的结果。这些结果的直接后果是一个身份的欧拉特征和当地的同构有限性定理。
We prove bubble-tree convergence of sequences of gradient Ricci shrinkers with uniformly bounded entropy and uniform local energy bounds, refining the compactness theory of Haslhofer and Müller (Geom Funct Anal 21:1091–1116, 2011; Proc Am Math Soc 143(10):4433–4437, 2015). In particular, we show that no energy concentrates in neck regions, a result which implies a local energy identity for the sequence. Direct consequences of these results are an identity for the Euler characteristic and a local diffeomorphism finiteness theorem.