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Counterexamples to prescribed scalar curvature in the null case
Yuxiang Li, Yunqing Wu, Jie Zhou
We construct smooth functions on the flat torus that change sign and have negative mean but cannot be realized as the scalar curvature of any metric in the giv…
Estimates for complex singular Monge-Ampère equations via integral method
Yunqing Wu, Kai Zheng
In this paper, we obtain gradient estimates and Laplacian estimates for the solution to the singular complex Monge-Ampère equation by applying the integral method.
Prescribing positive curvature with conical singularities on
Jingyi Chen, Yuxiang Li, Yunqing Wu
For conformal metrics with conical singularities and positive curvature on , we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an o…
Prescribing negative curvature with cusps and conical singularities on compact surface
Jingyi Chen, Yuxiang Li, Yunqing Wu
On a compact surface, we prove existence and uniqueness of the conformal metric whose curvature is prescribed by a negative function away from finitely many points where the metric…
Classification of Willmore surfaces with vanishing Gaussian curvature
Yunqing Wu
We classify simply-connected, complete Willmore surfaces with vanishing Gaussian curvature. We also study the Willmore cones and give a classification. As an application, we give a…