English

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

Differential Geometry 2023-03-30 v2

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.

Keywords

Cite

@article{arxiv.2206.06791,
  title  = {Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers},
  author = {Reto Buzano and Louis Yudowitz},
  journal= {arXiv preprint arXiv:2206.06791},
  year   = {2023}
}

Comments

32 pages; v2: Final version after minor revision, to appear in Math. Z