MATRIX HARNACK ESTIMATES FOR A PARABOLIC EQUATION ON COMPACT KÄHLER MANIFOLDS

MATRIX HARNACK ESTIMATES FOR A PARABOLIC EQUATION ON COMPACT KÄHLER MANIFOLDS

We prove matrix and classical Harnack estimates for a positive solution to the parabolic equation ∂_tu(x, t) = ∆u(x, t) + A(u(x, t)) on a compact Kähler manifold. By tracing and integrating the matrix Harnack inequality, we obtain the classical Harnack estimate. We also give matrix and classical Harnack inequalities of two classes of specific parabolic equations, which extend existing results to more general cases.

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