arXiv:1011.2728 [math.DG]AbstractReferencesReviewsResources
The energy of a smooth metric measure space and applications
Published 2010-11-11, updated 2012-05-03Version 3
We introduce and study the notion of the energy of a smooth metric measure space, which includes as special cases the Yamabe constant and Perelman's $\nu$-entropy. We then investigate some properties the energy shares with these constants, in particular its relationship with the $\kappa$-noncollapsing property. Finally, we use the energy to prove a precompactness theorem for the space of compact quasi-Einstein smooth metric measure spaces, in the spirit of similar results for Einstein metrics and gradient Ricci solitons.
Comments: 44 pages; rewritten to use the more standard language of smooth metric measure spaces, and corrected some errors in the appendix
Categories: math.DG
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