Stochastic analysis on manifolds

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Entropies, convexity, and functional inequalities (2002, background): “5, Sect. 4]. Such a proof can be extended to paths spaces on manifolds as what was already done for the logarithmic Sobolev inequality in [CHL97, Wan96] (see also [ Hsu02 , Sect.”
Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds (2005, methodology): “Using the Laplace parison theorem in Riemannian geometry, the comparison theorem of one-dimen stochastic differential equations and the Itô–Skorokhod formula for the radial pa Brownian motion, Hsu [35,36] proved Theorem 1.”
Eigenvalues, inequalities and ergodic theory (2001, background): “Hua (1985, Part X), L. K. Hua and S. Hua (1985). The conclusion is that the system becomes more stable than the idealized model.”
Entropies, convexity, and functional inequalities : On Phi-entropies and Phi-Sobolev inequalities (2004, background): “5, Sect. 4]. Such a proof can be extended to paths spaces on manifolds as what was already done for the logarithmic Sobolev inequality in [CHL97, Wan96] (see also [ Hsu02 , Sect.”
Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow (2008, unknown): “We compute Li(t)Lj (t)(f ◦ π)(u) = ∇g(t) df (uei, uej ) as in [6].”