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| In this paper, we study the $(p, p)$-form solution to the Hodge Laplacian heat equation on a Kähler manifold. After establishing the preservation of $r$-positivity of such solution under some invariant curvature condition, %that the $r$-positivity of a $(p, p)$-form solution is preserved under some %invariant curvature condition, we prove a differential Harnack estimate (in the sense of Li-Yau-Hamilton) for the $r$-positive solutions of the Hodge Laplacian heat equation. We also prove a nonlinear version coupled with the Kähler-Ricci flow. |
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| Keywords:Kähler manifold; Hodge Laplacian heat equation; $(p, p)$-form; differential Harnack estimate |
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