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arXiv · 2309.17250

Liouville theorems for ancient solutions of subexponential growth to the heat equation on graphs

Bobo Hua·Wenhao Yang
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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.

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Bobo Hua, Wenhao Yang. 2023-09-29. Liouville theorems for ancient solutions of subexponential growth to the heat equation on graphs. https://arxiv.org/abs/2309.17250

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