Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 575-588 |
| Number of pages | 14 |
| Journal | Mathematical Research Letters |
| Volume | 19 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2012 |
Keywords
- Gradient estimate
- Hodge Laplacian
- Sobolev inequality