Séminaire de Géométrie

On the asymptotic Plateau problem in \(\mathbb E (-1,\tau)\)

by Mr Jésus Castro Infantes

1180 (Bât E2) (Tours)

1180 (Bât E2)



In this talk we will discuss about the asymptotic Plateau problem in the homogeneous \(3\)-manifold \(\mathbb E(−1, \tau )\) with \(4\)-dimensional isometry group. This mean that, given a collection \(\Gamma\) of simple curves in the asymptotic boundary of \(\mathbb E(−1, \tau )\), decide if there is an area minimizing or a minimal surface with asymptotic boundary \(\Gamma\). We will show that some of the results obtained in the product space \(\mathbb H^2 \times  \mathbb R\), which correspond with the case  \(\tau = 0\), can be extended to \(\mathbb E(−1, \tau )\).