Calculus of Variations and Geometric Measure Theory

R. Haslhofer - R. Müller

A note on the compactness theorem for 4d Ricci shrinkers

created by muller on 11 Aug 2014
modified on 12 Jun 2018


Submitted Paper

Inserted: 11 aug 2014
Last Updated: 12 jun 2018

Year: 2014

ArXiv: 1407.1683 PDF


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.