Gradient estimate for eigenforms of Hodge Laplacian

Details Gradient estimate for eigenforms of Hodge Laplacian Gradient estimate for eigenforms of Hodge Laplacian

2011-09-22

arxiv.org/abs/1109.4968v3

Mathematics

Differential Geometry

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Scientific paper

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.

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