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

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

2010-04-27

arxiv.org/abs/1004.4840v1

Mathematics

Differential Geometry

Scientific paper

In this paper we study the heat equation (of Hodge-Laplacian) deformation of $(p, p)$-forms on a K\"ahler 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 K\"ahler-Ricci flow and some interpolating matrix differential Harnack type estimates for both the K\"ahler-Ricci flow and the Ricci flow.

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