Spectral properties of reducible conical metrics

Bin Xu; Xuwen Zhu

doi:10.1215/00192082-9043431

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arXiv · 1909.00546

Spectral properties of reducible conical metrics

Bin Xu·Xuwen Zhu

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Abstract

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. We also give a lower bound of the first nonzero eigenvalue, and a complete classification of the eigenspace dimension depending on the monodromy. This paper can be seen as a new connection between the complex analysis method and the PDE approach in the study of spherical conical metrics.

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BibTeX RIS

Bin Xu, Xuwen Zhu. 2019-09-02. Spectral properties of reducible conical metrics. https://doi.org/10.1215/00192082-9043431

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