The rigidity of Ricci shrinkers of dimension four
Mathematics - Differential Geometry
Differential Geometry (math.DG)
FOS: Mathematics
53C
0101 mathematics
01 natural sciences
DOI:
10.1090/tran/7539
Publication Date:
2018-02-21T15:46:59Z
AUTHORS (2)
ABSTRACT
1 figure. Any comments are welcome<br/>In dimension $4$, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov-Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br/>
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