Extremal of Log-Sobolev Functionals and Li-Yau Estimate on ${\text{RCD}}^{\ast }(K,N)$ Spaces

Samuel Drapeau, Liming Yin

In this work, we study the extremal functions of the log-Sobolev functional on compact metric measure spaces satisfying the ${\mathrm{RCD}}^{\ast }(K,N)$ condition for $K$ in $\mathbb{R}$…