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arXiv · 2110.15580

Metrics with positive constant curvature and modular differential equations

Jia-Wei Guo·Chang-Shou Lin·Yifan Yang
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Abstract

In this paper, we consider the problem when a differential equation y"(z)=Q(z)y(z) is Fuchsian on H* and apparent on H, where Q(z) is a meromorphic modular form of weight 4 on SL(2,Z) and H denotes the complex upper half-plane. Such a problem is closely related to the problem of the existence of a conformal metric with curvature 1/2 on H.

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Jia-Wei Guo, Chang-Shou Lin, Yifan Yang. 2021-10-29. Metrics with positive constant curvature and modular differential equations. https://arxiv.org/abs/2110.15580

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