On the structure of almost Einstein manifolds

Tian, Gang; Wang, Bing

doi:10.1090/jams/834

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.

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