Parabolic frequency on Ricci flows
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classification
math.DG
math.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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