We prove some existence and nonexistence results for complete area minimizing surfaces in the homogeneous space E(- 1 , τ). As one of our main results, we present sufficient conditions for a curve Γ in ∂∞E(- 1 , τ) to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in E(- 1 , τ) having Γ as its asymptotic boundary.
All Science Journal Classification (ASJC) codes
- Political Science and International Relations
- Geometry and Topology
- Area minimizing surfaces
- Asymptotic Plateau problem
- Asymptotic boundary
- E(κ, τ) spaces