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arXiv · 1603.02989

A weighted renormalized curvature for manifolds with density

Jeffrey S. Case
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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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Jeffrey S. Case. 2016-03-09. A weighted renormalized curvature for manifolds with density. https://arxiv.org/abs/1603.02989

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