Speaker: 刘忠原教授，河南大学

Title: Some results on singular solutions for the Liouville type equation

Language: Chinese

Time & Venue: 2024.12.05 15:30-16:30 腾讯会议：584-515-980

Abstract: In this talk, we introduce some recent results on asymptotic behavior of singular solutions for the Liouville type equation. More precisely, we establish asymptotic expansions up to arbitrary orders of singular solution near the isolated singular point. This provides asymptotic expansions near an isolated singular point for conformally flat metrics with constant positive Q-curvature. We also construct a family of radial and non-radial singular solutions of the Liouville equation in a punctured disc via the fixed point argument. To construct the singular solutions, we need to understand the prescribed asymptotic expansions at the isolated singular point of a singular solution for the Liouville equation.