Paper · Mar 9, 2016
A weighted renormalized curvature for manifolds with density
As on arXiv
Abstract
We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are stable with respect to the associated -functional.
- Submitted
- Mar 9, 2016
- Subjects
- math.DG
Comments: 10 pages
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Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.