The asymptotic Plateau problem in Gromov hyperbolic manifolds

  • Urs Lang
Original article

DOI: 10.1007/s005260100140

Cite this article as:
Lang, U. Calc Var (2003) 16: 31. doi:10.1007/s005260100140

Abstract.

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.

Mathematics Subject Classification (2000):49Q05, 53A10 

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Urs Lang
    • 1
  1. 1.Departement Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland (e-mail: lang@math.ethz.ch) CH

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