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

DOI10.1007/S00209-023-03272-ZarXiv2206.06791MaRDI QIDQ6402037

Publication date: 14 June 2022

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.

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Ricci flows (53E20)

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