Driver, Bruce K.; Hu, Yaozhong On heat kernel logarithmic Sobolev inequalities. (English) Zbl 0918.60039 Davies, I. M. (ed.) et al., Stochastic analysis and applications. Proceedings of the 5th Gregynog symposium, Gregynog, Powys, GB, July 9-14, 1995. Singapore: World Scientific. 189-200 (1996). Summary: This note is devoted to a pedagogical proof of logarithmic Sobolev inequalities on compact Riemannian manifolds when the reference measure is taken to be a heat kernel measure. The inequalities explained in this paper seem to have been first discovered by D. Bakry and M. Ledoux [Private communication in Nov. 1994 at the Taniguchi Symp., held in England].For the entire collection see [Zbl 0901.00050]. Cited in 6 Documents MSC: 60H07 Stochastic calculus of variations and the Malliavin calculus 47J20 Variational and other types of inequalities involving nonlinear operators (general) 58J35 Heat and other parabolic equation methods for PDEs on manifolds Keywords:logarithmic Sobolev inequalities; Riemannian manifolds; heat kernel measure PDFBibTeX XMLCite \textit{B. K. Driver} and \textit{Y. Hu}, in: Stochastic analysis and applications. Proceedings of the 5th Gregynog symposium, Gregynog, Powys, GB, July 9-14, 1995. Singapore: World Scientific. 189--200 (1996; Zbl 0918.60039)