Gaussian densities and stability for some Ricci solitons

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dc.creatorCao, Huai-Dong
dc.creatorHamilton, Richard S.
dc.creatorIlmanen, Tom
dc.date2004-04-07
dc.date.accessioned2026-07-07T05:07:16Z
dc.date.available2026-07-07T05:07:16Z
dc.descriptionIn this announcement, we exhibit the second variation of Perelman's $λ$ and $ν$ functionals for the Ricci flow, and investigate the linear stability of examples. We also define the "central density" of a shrinking Ricci soliton and compute its values for certain examples in dimension 4. Using these tools, one can sometimes predict or limit the formation of singularities in the Ricci flow. In particular, we show that certain Einstein manifolds are unstable for the Ricci flow in the sense that generic perturbations acquire higher entropy and thus can never return near the original metric.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0404165
dc.identifierhttp://arxiv.org/abs/math/0404165
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70793
dc.subjectDifferential Geometry
dc.titleGaussian densities and stability for some Ricci solitons
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