Calculus of Variations and Geometric Measure Theory

R. Haslhofer - R. Buzano

A note on the compactness theorem for 4d Ricci shrinkers

created by muller on 12 Jun 2018
modified on 13 Jun 2022


Published Paper

Inserted: 12 jun 2018
Last Updated: 13 jun 2022

Journal: Proceedings of the American Mathematical Society
Volume: 143
Year: 2015
Doi: 10.1090/proc/12648

ArXiv: 1407.1683 PDF

Note name change of one author from Reto Müller to Reto Buzano in 2015. Please cite as Haslhofer-Müller. Name changed here in order to import to author page correctly.


In arXiv:1005.3255 we proved an orbifold Cheeger-Gromov compactness theorem for complete 4d Ricci shrinkers with a lower bound for the entropy, an upper bound for the Euler characterisic, and a lower bound for the gradient of the potential at large distances. In this note, we show that the last two assumptions in fact can be removed. The key ingredient is a recent estimate of Cheeger-Naber arXiv:1406.6534.