Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on Kähler manifolds

Abstract

In this paper we study the heat equation (of Hodge-Laplacian) deformation of $(p,p)$-forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a $(p,p)$-form solution is preserved under such an invariant condition we prove the sharp differential Harnack (in the sense of Li-Yau-Hamilton) estimates for the positive solutions of the Hodge-Laplacian heat equation. We also prove a nonlinear version coupled with the Kähler-Ricci flow and some interpolating matrix differential Harnack type estimates for both the Kähler-Ricci flow and the Ricci flow.

References in corpus (1)

• Positive Complex Sectional Curvature, Ricci Flow and the Differential Sphere Theorem