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arXiv · 1011.2728

The energy of a smooth metric measure space and applications

Jeffrey S. Case
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Abstract

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.

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Jeffrey S. Case. 2010-11-11. The energy of a smooth metric measure space and applications. https://arxiv.org/abs/1011.2728

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