preprint
Inserted: 17 oct 2023
Last Updated: 17 oct 2023
Year: 2020
Abstract:
We show a triviality result for "pointwise" monotone in time, bounded
"eternal" solutions of the semilinear heat equation \begin{equation}
u{t}=\Delta u +
u
{p} \end{equation} on complete Riemannian manifolds of
dimension $n \geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than
the critical Sobolev exponent $\frac{n+2}{n-2}$.