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Mathematics > Differential Geometry

arXiv:1409.3251 (math)
[Submitted on 10 Sep 2014]

Title:On the linear stability of expanding Ricci solitons

Authors:Michael Jablonski, Peter Petersen, Michael Bradford Williams
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Abstract:In previous work, the authors studied the linear stability of algebraic Ricci solitons on simply connected solvable Lie groups (solvsolitons), which are stationary solutions of a certain normalization of Ricci flow. Many examples were shown to be linearly stable, leading to the conjecture that all solvsolitons are linearly stable. This paper makes progress towards that conjecture, showing that expanding Ricci solitons with bounded curvature (including solvsolitons) are linearly stable after extension by a Gaussian soliton. As in the previous work, the dynamical stability follows from a generalization of the techniques of Guenther, Isenberg, and Knopf.
Comments: 11 pages
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:1409.3251 [math.DG]
  (or arXiv:1409.3251v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1409.3251

Submission history

From: Michael Bradford Williams [view email]
[v1] Wed, 10 Sep 2014 20:36:08 UTC (11 KB)
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