Mathematical Research Letters
Volume 19 (2012)
Gradient estimate for eigenforms of Hodge Laplacian
Pages: 575 – 588
In this paper, we derive a gradient estimate for 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.
Hodge Laplacian, gradient estimate, Sobolev inequality
2010 Mathematics Subject Classification