On the zero-in-the-spectrum conjecture
Differential Geometry
2007-05-23 v1 Spectral Theory
Abstract
We prove that the answer to the "zero-in-the-spectrum" conjecture, in its form, suggested by J. Lott, is negative. Namely, we show that for any n > 5 there exists a closed n-dimensional manifold M, 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 of M.
Cite
@article{arxiv.math/9911077,
title = {On the zero-in-the-spectrum conjecture},
author = {M. Farber and S. Weinberger},
journal= {arXiv preprint arXiv:math/9911077},
year = {2007}
}
Comments
13 pages