Gradient estimate for eigenforms of Hodge Laplacian
  In this paper, we derive a gradient estimate for the linear combinations of eigenforms of the Hodge Laplacian on a closed manifold. The estimate is given in terms of the dimension, volume, diameter and curvature bound of the manifold. As an application, we obtain directly a sharp estimate for the heat kernel of the Hodge Laplacian. 
Jiaping Wang and Linfeng Zhou
math.DG