Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers
arXiv:2206.06791 · doi:10.1007/s00209-023-03272-z
Abstract
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.
32 pages; v2: Final version after minor revision, to appear in Math. Z