【时间】
2026年11月6日
【地点】
智华楼217
【会议安排】
09:00–09:30 Registration
09:30–10:15 Very singular solutions to the complex Monge–Ampère equation
王文龙（南开大学）
10:15–10:40 Tea break
10:40–11:25 Critical mean field equations for equilibrium turbulence with sign-changing prescribed
functions
朱晓宝（中国人民大学）
11:25–12:10 Solutions of the singular Yamabe problem near singular boundaries
沈伟明（首都师范大学）
12:10–14:00 Lunch
【会议报告摘要】
Very singular solutions to the complex Monge–Ampère equation
王文龙（南开大学）
Using partial Legendre transforms and a holomorphic pullback, we construct singular solutions to the complex Monge–Ampère equation with constant right-hand side in the Bedford–Taylor sense. For n ≥ 2, these solutions include: (1) a bounded solution on Dⁿ that is discontinuous almost everywhere and nowhere classically differentiable; (2) a continuous exhaustion of Cⁿ that does not belong to W²,¹_loc(Cⁿ); and (3) a continuous solution on the closure of Dⁿ whose Laplacian has a singular part.
Critical mean field equations for equilibrium turbulence with sign-changing prescribed functions
朱晓宝（中国人民大学）
This talk presents a new existence result for mean field equations in equilibrium turbulence, focusing on the critical case with sign-changing prescribed functions. The result generalizes earlier work of Chunqin Zhou (Nonlinear Analysis 69, 2008), which treated constant prescribed functions. This is joint work with Linlin Sun.
Solutions of the singular Yamabe problem near singular boundaries
沈伟明（首都师范大学）
This talk discusses the asymptotic behavior of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derives optimal estimates. The background metrics are not assumed to be conformally flat.
