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Let M be a cg-connected manifold. Let L be a second-order differential operator with real cg(R) coefficients on M and such that L1 0 (i.e., L has no zero-order term). Assume that there exists a posi...
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties o...
By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong...
We consider a subset $S$ of the complex Lie algebra $\so(n,\C)$ and the cone $C(S)$ of curvature operators which are nonnegative on $S$. We show that $C(S)$ defines a Ricci flow invariant curvature co...
In this paper, we prove several differential Harnack inequalities for positive solutions of nonlinear (backward) heat equations with different potentials under the Ricci flow. In particular, for a clo...

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