Sharp differential estimates of Li-Yau-Hamilton type for positive $p,p$-forms on Kähler manifolds - Mathematics > Differential GeometryReport as inadecuate




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Abstract: 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 andestablishing that the positivity of a $p, p$-form solution is preserved undersuch an invariant condition we prove the sharp differential Harnack in thesense of Li-Yau-Hamilton estimates for the positive solutions of theHodge-Laplacian heat equation. We also prove a nonlinear version coupled withthe K\-ahler-Ricci flow and some interpolating matrix differential Harnack typeestimates for both the K\-ahler-Ricci flow and the Ricci flow.



Author: Lei Ni, Yanyan Niu

Source: https://arxiv.org/







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