| Abstract: |
| We consider the Liouville equation $\Delta u +\lambda^2 e^{\,u}=0$ with the Dirichlet boundary conditions in a two dimensional, doubly connected domain $\Omega$. We show that there exists a simple, closed curve $\gamma\in \Omega$ such that for a sequence $\lambda_n\to 0$ there exist a sequence of solutions $u^{max}_{\lambda_n}$ such that $\frac{\lambda_n^2}{\log\frac{1}{\lambda_n}}\int_\Omega e^{\,u^{max}_{\lambda_n}}\,dx\to c_0|\gamma|$. |
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