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First variation of the Log Entropy functional along the Ricci flow
Junfang Li
In this note, we establish the first variation formula of the adjusted log entropy functional introduced by Ye in \cite{Y2}. As a direct consequence, we also obtain…
Monotonicity formulas under rescaled Ricci flow
Jun-Fang Li
In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem \ref{theo rescaled}.
The quermassintegral inequalities for starshaped domains
Pengfei Guan, Junfang Li
We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt \cite{G} and Urbas \cite{U} on an expandi…
Eigenvalues and energy functionals with monotonicity formulae under Ricci flow
Junfang Li
In this note, we construct families of functionals of the type of -functional and -functional of Perelman. We prove that these new functionals are nondecr…