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arXiv · 2206.06791

Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers

Reto Buzano·Louis Yudowitz
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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.

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Reto Buzano, Louis Yudowitz. 2022-06-14. Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers. https://doi.org/10.1007/s00209-023-03272-z

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