arXiv subjects
Publications and source records attributed to 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 has prescribed angles presenting cusps or conical singularities.
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.
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.
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 Bernstein-type theorem.