M. Farber
On the zero-in-the-spectrum conjecture
Farber, M.; Weinberger, S.
Authors
S. Weinberger
Abstract
We prove that the answer to the "zero-in-the-spectrum" conjecture, in the form suggested by J. Lott, is negative. Namely, we show that for any $n\ge 6$ there exists a closed $n$-dimensional smooth manifold $M^n$, so that zero does not belong to the spectrum of the Laplace-Beltrami operator acting on the $L^2$ forms of all degrees on the universal covering $\tilde M$.
Citation
Farber, M., & Weinberger, S. (2001). On the zero-in-the-spectrum conjecture. Annals of Mathematics, 154(1), 139 - 154. https://doi.org/10.2307/3062113
Journal Article Type | Article |
---|---|
Publication Date | 2001-07 |
Deposit Date | May 1, 2007 |
Journal | Annals of Mathematics |
Print ISSN | 0003-486X |
Publisher | Department of Mathematics |
Peer Reviewed | Peer Reviewed |
Volume | 154 |
Issue | 1 |
Pages | 139 - 154 |
DOI | https://doi.org/10.2307/3062113 |
Publisher URL | http://annals.math.princeton.edu/issues/2001/154_1.html |
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