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A weighted renormalized curvature for manifolds with density


Author: Jeffrey S. Case
Journal: Proc. Amer. Math. Soc. 145 (2017), 4031-4040
MSC (2010): Primary 53C21; Secondary 53C25, 58E11
DOI: https://doi.org/10.1090/proc/13566
Published electronically: March 23, 2017
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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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Additional Information

Jeffrey S. Case
Affiliation: Department of Mathematics, Pennsylvania State University, 109 McAllister Building, University Park, Pennsylvania 16802
Email: jscase@psu.edu

DOI: https://doi.org/10.1090/proc/13566
Keywords: Smooth metric measure space, manifold with density, renormalized volume, gradient Ricci soliton, $\mathcal{W}$-functional
Received by editor(s): April 1, 2016
Received by editor(s) in revised form: September 30, 2016
Published electronically: March 23, 2017
Communicated by: Lei Ni
Article copyright: © Copyright 2017 American Mathematical Society

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