Boundary Behaviors for Liouville's Equation in Planar Singular Domains

2015/11/03 by Qing Han, Weiming Shen, Han, Qing +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1511.01149

Accepted by Journal of Functional Analysis

openalex publication_date 2015/11/03 · arxiv created 2017/08/22 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary. The conformal structure plays an essential role.

Citations

• Existence an regularity of constant mean curvature hypersurfaces in hyperbolic space

Related

• Asymptotic behavior of complete conformal metric near singular boundary
• The geometric Neumann problem for the Liouville equation
• Local and nonlocal singular Liouville equations in Euclidean spaces
• Solutions of the singular Yamabe problem near singular boundaries
• Metrics of constant curvature on a Riemann surface with two corners on the boundary