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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...
Large Harnack inequalities, Kobayashi distances and holomorphic motions
Large Harnack inequalities Kobayashi distances holomorphic motions Complex Variables
2012/4/18
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...
Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
Harnack inequality functional solution delay SDE strong Feller property
2011/2/28
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...
A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
Lie algebraic Ricci flow invariant curvature conditions Harnack inequalities
2010/11/22
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...
Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
Differential Harnack inequality Interpolated Harnack inequality Nonlinear
2010/12/1
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...