First variation of the Log Entropy functional along the Ricci flow

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143655In this note, we establish the first variation formula of the adjusted log entropy functional $\mathcal Y_a$ introduced by Ye in \cite{Y2}. As a direct consequence, we also obtain the monotonicity of $\mathcal Y_a$ along the Ricci flow.4 pages. One remark improvedDifferential GeometryAnalysis of PDEs53C20, 53C21First variation of the Log Entropy functional along the Ricci flowtext