The asymptotic Plateau problem in Gromov hyperbolic manifolds
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- Lang, U. Calc Var (2003) 16: 31. doi:10.1007/s005260100140
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We solve the asymptotic Plateau problem in every Gromov hyperbolic Hadamard manifold (X,g) with bounded geometry. That is, we prove existence of complete (possibly singular) k-dimensional area minimizing surfaces in X with prescribed boundary data at infinity, for a large class of admissible limit sets and for all \(2 \le k < dim X\). The result also holds with respect to any riemannian metric \(\tilde g\) on X which is lipschitz equivalent to g.