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

Patricia Klaser , UFRGSBrazil
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.