The asymptotic Plateau problem in Gromov hyperbolic manifolds |
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Authors: | Lang Urs |
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Institution: | (1) Departement Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland (e-mail: lang@math.ethz.ch) , CH |
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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 . The result also holds with respect to any riemannian metric on X which is lipschitz equivalent to g.
Received: 23 January 2001 / Accepted: 25 October 2001 Published online: 28 February 2002 |
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Keywords: | Mathematics Subject Classification (2000):49Q05 53A10 |
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