The energy of a conformal warped manifold and applications

Details The energy of a conformal warped manifold and applications The energy of a conformal warped manifold and applications

2010-11-11

arxiv.org/abs/1011.2728v2

Mathematics

Differential Geometry

53 pages; fixed minor mistakes and improved exposition of Section 6

Scientific paper

We introduce and study the notion of the energy of a conformally warped manifold, 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 quasi-Einstein metrics, in the spirit of similar results for Einstein metrics and gradient Ricci solitons.

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