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Perelman's entropy and heat kernel bounds on RCD spaces

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arxiv 2503.03017 v1 pith:ANVDYXHE submitted 2025-03-04 math.DG

classification math.DG
keywords spacesboundsheatperelmanw-entropyadditionallybakry-below
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We study Perelman's W-entropy functional on finite-dimensional RCD spaces, a synthetic generalization of spaces with Bakry-\'{E}mery Ricci curvature bounded from below. We rigorously justify the formula for the time derivative of the W-entropy and derive its monotonicity and rigidity properties. Additionally, we establish bounds for solutions of the heat equation, which are of independent interest.

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