Nelia Charalambous -- The form spectrum of open manifolds
Author information
- Nelia Charalambous
- University of Cyprus
- Website: http://euclid.mas.ucy.ac.cy/~nelia/index.html
Abstract:
The computation of the essential spectrum of the Laplacian requires the construction of a large class of test differential forms. On a general open manifold this is a difficult task, since there exists only a small collection of canonically defined differential forms to work with. In our work with Zhiqin Lu, we compute the essential k-form spectrum over asymptotically flat manifolds by combining two methods: First, we introduce a new version of the generalized Weyl criterion, which greatly reduces the regularity and smoothness of the test differential forms; second, we make use of Cheeger-Fukaya-Gromov theory and Cheeger-Colding theory to obtain a new type of test differential forms at the ends of the manifold. The generalized Weyl criterion can also be used to obtain other interesting facts about the k-form essential spectrum over an open manifold. Finally, we present some recent results on the form spectrum of negatively curved manifolds.