Liouville theorems for ancient caloric functions via optimal growth conditions

Mosconi, Sunra

doi:10.1090/proc/15245

Liouville theorems for ancient caloric functions via optimal growth conditions
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Proc. Amer. Math. Soc. 149 (2021), 897-906 Request permission

Abstract:

We prove two Liouville theorems for ancient nonnegative solutions of the heat equation on a complete noncompact Riemannian manifold with Ricci curvature bounded from below by $-K$, $K\geqslant 0$. If, at any fixed time, such a solution grows subexponentially in space, then it is either constant (when $K=0$) or stationary (if $K>0$). We also show the optimality of this growth condition through examples.

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