Differential geometric analysis establishes Sobolev inequalities along the Ricci-Bourguignon flow, revealing heat kernel upper bounds and noncollapsing estimates.
Consider a closed Riemannian manifold M where the metrics $g(t)$ evolve by the Ricci-Bourguignon flow (RBF).The paper first derives a Sobolev inequality along the RBF. Then, by applying this Sobolev inequality we obtain a linear parabolic estimate and an upper bound estimate for the heat kernel along the RBF. Additionally, it confidently investigates the κ-noncollapsing estimates along the RBF.
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Jafari et al. (2026) studied this question.
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