A logarithmic Sobolev form of the Li-Yau parabolic inequality (Q879634)

In the very interesting paper under review the authors present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators which contains and improves the Li-Yau parabolic inequality from [\textit{P. Li} and \textit{S. T. Yau}, Acta Math. 156, 154--201 (1986; Zbl 0611.58045)]. That new inequality is of interest already in Euclidean space for the standard Gaussian measure and the result may also be seen as an extended version of the semigroup commutator properties under curvature conditions.