Lei Zhang, Texas A&M University Classification theorems on a prescribing Gauss curvature and geodesic curvature problem.

\underline{Abstract}: For different constants a, b, we give a classification of all smooth solutions of

\{ \begin{matrix}Δu + ae^{u} = 0 & ℝ_{+}^{2} \\ \frac{∂u}{∂y} = be^{\frac{u}{2}} & ∂ℝ_{+}^{2} \end{matrix} under integral-finiteness assumptions (A) = ∫_{ℝ_{+}^{2}} e^{u} < ∞ or (B) =

∫_{∂ℝ_{+}^{2}} e^{\frac{u}{2}} < ∞. This classification finds all confirmal metrics to the standard (R_{+}^{2}, δ) with

constant Gauss curvature and constant geodesic curvature on the boundary ∂ℝ_{+}^{2} under (A) or (B).