Existence and non existence of complete area minimizing surfaces in $mathbb{E}(-1,tau)$.

Início: 29/10/2020 17:00

Término: 29/10/2020 18:00

Palestrante: Álvaro Krüger Ramos (Universidade Federal do Rio Grande do Sul)

E-mail do Palestrante:

Resumo: Recall that $mathbb{E}(-1,tau)$ is a homogeneous space with four-dimensional isometry group which is given by the total space of a fibration over $mathbb{H}^2$ with bundle curvature $tau$. Given a finite collection of simple closed curves in $partial_{infty}|mathbb{E}(-1,tau)$, we provide sufficient conditions on $Gamma$ so that there exists an area minimizing surface $Sigma$ in $mathbb{E}(-1,tau)$ with asymptotic boundary $Gamma$. We also present necessary conditions for such a surface $Sigma$ to exist. This is joint work with P. Klaser and A. Menezes.