The Dirichlet problem for the constant mean curvature equation in Sol$_3$

The Dirichlet problem for the constant mean curvature equation in Sol$_3$

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Patricia Klaser , UFRGS-Brazil
Fine Hall 314

Please note different day (Thursday).   The Dirichlet problem for CMC surfaces with infinite boundary data was first studied for minimal graphs in $\mathbb{R}^3$ by Jenkins and Serrin and then by Sprück for CMC $H$ surfaces. The existence results, which consist in giving necessary and sufficient conditions on a domain for it to admit a solution to the problem were later obtained for different ambient spaces such as $\mathbb{H}^3,$ $\mathbb{H}^2 \times \mathbb{R},$ $\mathbb{S}^2 \times \mathbb{R},$ among others. In this talk we will describe some existence results for the Dirichlet problem in Sol$_3.$ This is a joint work with Ana Menezes.