A weighted renormalized curvature for manifolds with density

Case, Jeffrey

doi:10.1090/proc/13566

A weighted renormalized curvature for manifolds with density
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by Jeffrey S. Case PDF

Proc. Amer. Math. Soc. 145 (2017), 4031-4040 Request permission

Abstract:

We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient $v_3$ in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are stable with respect to the associated $\mathcal {W}$-functional.

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