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We construct stable solutions of $\Delta u + \lambda e^u=0$ with Dirichletboundary conditions in small tubular domains (i.e. geodesic$\varepsilon$--neighbourhoods of a curve $\Lambda$ embedded in $\mathbb{R}^n$),adapting the arguments of Pacard-Pacella-Sciunzi. We also show unicity of thesesolutions, in particular, we show that the stable branch of the bifurcationdiagram is similar to the well-known nose-shaped diagram of the standardGelfand problem in the unit ball. In this work, $\Lambda$ can be replaced byany compact smooth manifold embedded in $\mathbb{R}^n$.

The Gelfand Problem in Tubular Domains