论文标题
泡沫收敛和局部差异性有限性的梯度ricci收缩术
Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers
论文作者
论文摘要
我们证明了梯度RICCI收缩序列的气泡-tree收敛，具有均匀界限的熵和统一的局部能量边界，从而完善了Haslhofer-Mueller的紧凑性理论。特别是，我们表明没有能量集中在颈部区域，这意味着序列的局部能量身份。这些结果的直接后果是欧拉特征和局部差异有限定理的身份。
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-Mueller. 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.
