A weighted renormalized curvature for manifolds with density

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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Bibliographic Details
Published in:	Proceedings of the American Mathematical Society Vol. 145; no. 9; pp. 4031 - 4040
Main Author:	CASE, JEFFREY S.
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-09-2017
Subjects:	D. GEOMETRY mathcal{W\|$-functional Smooth metric measure space renormalized volume gradient Ricci soliton manifold with density
Online Access:	Get full text
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Description
Summary:	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.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/proc/13566