# Band width estimates via the Dirac operator

@article{Zeidler2019BandWE, title={Band width estimates via the Dirac operator}, author={Rudolf Zeidler}, journal={arXiv: Differential Geometry}, year={2019} }

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $\sigma > 0$, the distance between the boundary components of $V$ is at most $C/\sqrt{\sigma}$, where $C < 8 + 4\pi$ is a universal constant. This verifies a conjecture of Gromov for such manifolds. In particular, our result applies to all high-dimensional closed simply… CONTINUE READING

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