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arXiv · 2408.12201

Prescribing positive curvature with conical singularities on $\mathbb S^2$

Jingyi Chen·Yuxiang Li·Yunqing Wu
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Abstract

For conformal metrics with conical singularities and positive curvature on $\mathbb S^2$, we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is a fine analysis of the bubble trees and an area identity in the convergence process.

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Jingyi Chen, Yuxiang Li, Yunqing Wu. 2024-08-22. Prescribing positive curvature with conical singularities on $\mathbb S^2$. https://arxiv.org/abs/2408.12201

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