Mathematical Research Letters

Volume 19 (2012)

Number 3

Gradient estimate for eigenforms of Hodge Laplacian

Pages: 575 – 588



Jiaping Wang (School of Mathematics, University of Minnesota)

Linfeng Zhou (Department of Mathematics, East China Normal University, Shanghai, China)


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


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