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arXiv · 1810.05073

$\sigma_2$ Yamabe problem on conic 4-spheres

Hao Fang·Wei Wei
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Abstract

We discuss the constant $\sigma_{2}$ problem for conic 4-spheres. Based on earlier works of Chang-Han-Yang and Han-Li-Teixeira, we are able to find a necessary condition for the existence problem. In particular, when the condition is sharp, we have the uniqueness result similar to that of Troyanov in dimension 2. It indicates that the boundary of the moduli of all conic 4-spheres with constant $\sigma_{2}$ metrics consists of conic spheres with 2 conic points and rotational symmetry.

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Hao Fang, Wei Wei. 2018-10-11. $\sigma_2$ Yamabe problem on conic 4-spheres. https://arxiv.org/abs/1810.05073

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