Corpus ID: 160009855

Band width estimates via the Dirac operator

  title={Band width estimates via the Dirac operator},
  author={Rudolf Zeidler},
  journal={arXiv: Differential Geometry},
  • Rudolf Zeidler
  • Published 2019
  • Mathematics
  • arXiv: Differential Geometry
  • 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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