Spectral properties of reducible conical metrics

17 Sep 2019 Xu Bin Zhu Xuwen

We show that the monodromy of a spherical conical metric is reducible if and only if it has a real-valued eigenfunction with eigenvalue 2 in the holomorphic extension of the associated Laplace--Beltrami operator. Such an eigenfunction produces a meromorphic vector field, which is then related to the developing maps of the conical metric... (read more)

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Categories


  • DIFFERENTIAL GEOMETRY
  • ANALYSIS OF PDES
  • SPECTRAL THEORY