Time-Analyticity of solutions to the ricci flow

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Abstract

We prove that if g(t) is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on M ×[0,Ω], then the correspondence t ↦ g(t) is real-analytic at each t0 ∈ (0,Ω). The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial derivatives of the curvature tensor, which we further use to show that, under the above global hypotheses, for any x0 ∈M and t<inf>0</inf> ∈ (0,Ω), there exist local coordinates x = x<sup>i</sup> on a neighborhood U ⊂ M of x<inf>0</inf> in which the representation gij (x,t) of the metric is real-analytic in both x and t on some cylinder U ×(t<inf>0</inf> −∈, t<inf>0</inf> +∈).

Original languageEnglish (US)
Pages (from-to)535-576
Number of pages42
JournalAmerican Journal of Mathematics
Volume137
Issue number2
StatePublished - 2015

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Ricci Flow
Analyticity
Curvature Tensor
Correspondence
Curvature
Derivative
Metric
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Time-Analyticity of solutions to the ricci flow. / Kotschwar, Brett.

In: American Journal of Mathematics, Vol. 137, No. 2, 2015, p. 535-576.

Research output: Contribution to journalArticle

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