Propagation of symmetries for Ricci shrinkers

We will show that if a gradient shrinking Ricci soliton has an approximate symmetry on one scale, this symmetry propagates to larger scales. This is an example of the shrinker principle which roughly states that information radiates outwards for shrinking solitons.

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Bibliographic Details
Published in:Advanced nonlinear studies 2023-06, Vol.23 (1), p.37-55
Main Authors: Colding, Tobias Holck, Minicozzi II, William P.
Format: Article
Language:English
Subjects:
53E20
Ricci flow
solitons
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Description
Summary:We will show that if a gradient shrinking Ricci soliton has an approximate symmetry on one scale, this symmetry propagates to larger scales. This is an example of the shrinker principle which roughly states that information radiates outwards for shrinking solitons.
ISSN:2169-0375
2169-0375
DOI:10.1515/ans-2022-0071