Singular Solutions of the Loewner-Nirenberg Problem in Conic Domains with Prescribed Singularity at Vertices

2025/10/13 by Stephen Zhou, Zhou, Stephen
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2510.12010

Abstract

We study positive singular solutions of the Loewner-Nirenberg problem on conical domains and establish the existence of solutions that admit prescribed asymptotic expansions near vertices, valid to arbitrarily high order of approximation.

Citations

• The Loewner-Nirenberg Problem in Cones
• Singular solutions to the Yamabe equation with prescribed asymptotics
• Asymptotic expansions of solutions of the Yamabe equation and the σ_k-Yamabe equation near isolated singular points
• The Loewner-Nirenberg problem in singular domains
• Refined asymptotics for constant scalar curvature metrics with isolated singularities
• Constant scalar curvature metrics with isolated singularities
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

Related

• The Loewner-Nirenberg problem in singular domains
• Boundary expansion for the Loewner-Nirenberg problem in domains with conic singularities
• The Loewner-Nirenberg Problem in Cones
• Nodal solutions of the Brezis-Nirenberg problem in dimension 6
• Existence and non existence results for the singular Nirenberg problem