Title: Flow Decomposition, capacity inequalities, and Lane--Emden Inequalities on Weighted Graphs

Speaker: 黄学平（南京信息工程大学）

Time：2026年7月29日 9:00-10:00

Classroom：5107

Abstract:

We study Liouville-type theorems for the superlinear Lane–Emden inequality on weighted graphs. Under a mild completeness assumption, we show that sharp integral volume growth criteria exclude the existence of positive solutions. The proofs rely crucially on a flow decomposition method from network theory and probability. Along the way, we obtain relative capacity inequalities that are of independent interest.