Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 145, Issue 9, Pages 4031-4040Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/13566
Keywords
Smooth metric measure space; manifold with density; renormalized volume; gradient Ricci soliton; W-functional
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We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient v3 in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are stable with respect to the associated W-functional.
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