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Parabolic frequency on Ricci flows

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arxiv 2201.05505 v2 pith:VSRXRKBU submitted 2022-01-14 math.DG math.AP

Julius Baldauf , Dain Kim This is my paper · ORCID
classification math.DGmath.AP
keywords frequencyflowparabolicriccibackwardsmonotonicitysolutionsuniqueness
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This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple proof of backwards uniqueness. For solutions of more general parabolic equations on a Ricci flow, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.

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