17:45 Uhr | Magdalena Rodriguez (Granada) | Minimal surfaces in $\mathbb{H}^2\times\mathbb{R}$
Amidst the great activity in the past several years
concerning the study of complete minimal surfaces in homogeneous
three-manifolds, the study of minimal surfaces in $\mathbb{H}^2\times\mathbb{R}$ has witnessed
particular success. In this talk we will focus on complete minimal
surfaces with finite total curvature in $\mathbb{H}^2\times\mathbb{R}$. We will present the
construction of some important examples, the properties they have to
satisfy and the known classification results. Finally, we will
introduce non-proper complete minimal disks embedded in $\mathbb{H}^2\times\mathbb{R}$ which are
invariant by a vertical translation and have finite total curvature in
the quotient. They are a counterexample which shows that the
Calabi-Yau conjectures do not hold for embedded minimal surfaces in
$\mathbb{H}^2\times\mathbb{R}$.
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