Continuity of Dirac spectra

@article{Nowaczyk2013ContinuityOD,
  title={Continuity of Dirac spectra},
  author={Nikolai Nowaczyk},
  journal={Annals of Global Analysis and Geometry},
  year={2013},
  volume={44},
  pages={541-563}
}
  • N. Nowaczyk
  • Published 26 March 2013
  • Mathematics
  • Annals of Global Analysis and Geometry
It is well known that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article, we extend this result to a global version. We view the spectrum of a Dirac operator as a function $$\mathbb Z \,\rightarrow \mathbb R \,$$Z→R and endow the space of all spectra with an $$\mathrm{arsinh }$$arsinh-uniform metric. We prove that the spectrum of the Dirac operator depends continuously… 

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