Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on K\"ahler manifolds
Differential Geometry
2015-03-17 v1
Abstract
In this paper we study the heat equation (of Hodge-Laplacian) deformation of -forms on a K\"ahler manifold. After identifying the condition and establishing that the positivity of a -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.
Keywords
Cite
@article{arxiv.1004.4840,
title = {Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on K\"ahler manifolds},
author = {Lei Ni and Yanyan Niu},
journal= {arXiv preprint arXiv:1004.4840},
year = {2015}
}