Report Title: New Progress on the Classification and Liouville Properties of Solutions to Certain Quasilinear Elliptic Equations
Speaker: Professor Wang Youde
Affiliation: Guangzhou University
Time: 10:00–11:00, January 8, 2026
Venue: Tencent Meeting ID: 290-429-573
Abstract
In this talk, we will present the optimal Liouville theorem for the quasilinear degenerate Lane–Emden equation defined on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. We will also explain how to use the Nash–Moser iteration to derive optimal and unified Cheng–Yau-type gradient estimates for positive solutions of a class of quasilinear degenerate elliptic equations. In addition, we will discuss the classification and rigidity of positive solutions to the critical p-Laplace equation on complete noncompact Riemannian manifolds with nonnegative Ricci curvature.
Biography
Youde Wang is a professor and doctoral supervisor at Guangzhou University. He is a recipient of the National Science Fund for Distinguished Young Scholars and a selected member of the National Hundred, Thousand and Ten Thousand Talent Project. He has long been engaged in research on harmonic maps, geometric flows and related problems, and has achieved a series of academically significant results. He proposed the concept of Schrödinger–geometric flow, which has stimulated a large number of subsequent studies internationally, and was the first to establish its local well-posedness. He also solved open problems such as the validity of the energy identity for bubble formations arising from the convergence of sequences of α-harmonic maps.
