Parabolic Frequency on Ricci-Bourguignon flow and Yamabe flow
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Abstract
We analyze the evolution of certain parabolic-type energy expressions associated with linear heat-type equations in the setting of compact Riemannian manifolds undergoing the Ricci–Bourguignon and Yamabe flows. By formulating appropriate frequency-type quantities tailored to the underlying geometric dynamics, we demonstrate their monotonic nature under specific curvature assumptions and flow-adapted conditions. This study contributes to the understanding of the interaction between geometric evolution and analytic invariants.
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