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math.DG2006★ 1 cited
Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric
Dan Knopf, Andrea Young
We show that there exists a suitable neighborhood of a constant curvature hyperbolic metric such that, for all initial data in this neighborhood, the corresponding solution to a no…
math.DG2006
Local monotonicity and mean value formulas for evolving Riemannian manifolds
Klaus Ecker, Dan Knopf, Lei Ni +1
We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the fir…
math.DG2006★ 1 cited
Linear stability of homogeneous Ricci solitons
Christine Guenther, James Isenberg, Dan Knopf
As a step toward understanding the analytic behavior of Type-III Ricci flow singularities, i.e. immortal solutions that exhibit |Rm|<C/t curvature decay, we examine the linearizati…