## On the structure of almost Einstein manifolds

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- by Gang Tian and Bing Wang
- J. Amer. Math. Soc.
**28**(2015), 1169-1209 - DOI: https://doi.org/10.1090/jams/834
- Published electronically: June 17, 2015
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## Abstract:

In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense, and Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a sequence of almost Einstein manifolds has most properties which are known for the limit space of Einstein manifolds. As applications, we can apply our structure results to study the properties of Kähler manifolds.## References

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## Bibliographic Information

**Gang Tian**- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544; Beijing International Center for Mathematical Research, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 220655
- Email: tian@math.princeton.edu
**Bing Wang**- Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
- MR Author ID: 843464
- Email: bwang@math.wisc.edu
- Received by editor(s): February 24, 2013
- Received by editor(s) in revised form: September 29, 2014
- Published electronically: June 17, 2015
- Additional Notes: The first author was partially supported by NSF Grants DMS-0804095, DMS-1309359 and an NSFC Grant

The second author was partially supported by NSF Grant DMS-1006518 and funds from SCGP - © Copyright 2015 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**28**(2015), 1169-1209 - MSC (2010): Primary 53Cxx; Secondary 35Jxx
- DOI: https://doi.org/10.1090/jams/834
- MathSciNet review: 3369910