Abstract
Let Hpl (M) be the space of polynomial growth harmonic forms. We proved that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with a nonnegative curvature operator. In particular, this implies that the space of harmonic forms of fixed growth order on the Euclidean space with any periodic metric must be finite dimensional.
| Original language | English |
|---|---|
| Pages (from-to) | 167-183 |
| Number of pages | 17 |
| Journal | Journal of Differential Geometry |
| Volume | 73 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2006 |
| Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology