Sharp log-Sobolev inequalities in $\mathsf{CD}(0,N)$ spaces with applications

Zoltán M. Balogh, Alexandru Kristály, Francesca Tripaldi

Given $p,N>1,$ we prove the sharp $L^p$-log-Sobolev inequality on noncompact metric measure spaces satisfying the $\mathsf{CD}(0,N)$ condition, where the optimal constant involves the…