Backwards uniqueness of the Ricci flow

By Brett Kotschwar. 2009

84 citations recorded by the source corpus.

In this paper, we prove a unique continuation or ``backwards-uniqueness'' theorem for solutions to the Ricci flow. A particular consequence is that the isometry group of a solution cannot expand within the lifetime of the solution.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bacac632122749ea4b680cf68ab9290cb0492085

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

The local entropy along Ricci flow---Part A: the no-local-collapsing theorems (2017, background): “[28]) that the whole space-time M × [0, 1) is induced by the Gaussian soliton metric.”
Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, methodology): “) Nevertheless, as in [38], we can embed the problem into one for a prolonged “PDEODE” system of mixed differential inequalities for which an analog of”
On quotients of spaces with Ricci curvature bounded below (2017, background): “Conversely, by Kotschwar’s backward uniqueness of Ricci flow [50] also the converse inclusion holds; this gives that if (M, gt)t∈[0,T ] is a Ricci flow of complete metrics with bounded curvature, then the isometry group does not change along the flow, i.”