Speaker: 唐仲伟教授，北京师范大学

Inviter: 流体力学方程研究中心

Title: Some Recent Results on Nonlinear Problems on the Heisenberg Group

Language: Chinese

Time & Venue: 2026.05.07 10:30-11:30 南楼N204

Abstract: This talk is concerned with nonlinear equations involving sub-elliptic operators on the Heisenberg group. We first investigate the Bianchi–Egnell stability inequality associated with the sharp Sobolev inequality and establish the existence of a nontrivial minimizer by proving a strict inequality for the optimal stability constant. Second, we study the non-degeneracy of solutions to critical CR-Yamabe type problems on the Heisenberg group, as well as the existence of concentrating solutions to slightly subcritical equations involving the sub-Laplacian on bounded domains. Under suitable assumptions and for sufficiently small parameters, we construct sign-changing solutions with exactly two nodal domains. Finally, we establish the density and multiplicity of positive solutions to the prescribed Webster scalar curvature problem on the standard unit CR sphere. When the curvature function is asymptotically periodic on the Heisenberg group, we also prove the existence of infinitely many positive solutions. This is a joint work with Dr. Jiechen Qiang, Heming Wang, Bingwei Zhang and Yichen Zhang.