Séminaire de Géométrie

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

## by Mr Jésus Castro Infantes

Europe/Paris
1180 (Bât E2) (Tours)

### 1180 (Bât E2)

#### Tours

Description

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 $$\mathbb E(−1, \tau )$$.