A weighted renormalized curvature for manifolds with density
classification
🧮 math.DG
keywords
densityinvariantmanifoldsrenormalizedanalogousassociatedcoefficientconformal
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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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