Liouville theorems for ancient solutions of subexponential growth to the heat equation on graphs
arXiv:2309.17250
Abstract
Mosconi proved Liouville theorems for ancient solutions of subexponential growth to the heat equation on a manifold with Ricci curvature bounded below. We extend these results to graphs with bounded geometry: for a graph with bounded geometry, any nonnegative ancient solution of subexponential growth in space and time to the heat equation is stationary, and thus is a harmonic solution.
12 pages