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Weak density of smooth maps for the Dirichlet energy between manifolds

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Abstract.

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W 1,2(M,N) can be approximated weakly by smooth maps between M and N.

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Authors and Affiliations

  1. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22 - 26, 04103 Leipzig, Germany, e-mail: pakzad@mis.mpg.de, Deutschland

    M.R.. Pakzad

  2. D-Math, ETH Zentrum, 8092 Zürich, Switzerland, e-mail: riviere@math.ethz.ch, Switzerland

    T. Rivière

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  1. M.R.. Pakzad
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  2. T. Rivière
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Submitted: September 2002, Final version: November 2002.

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Pakzad, M., Rivière, T. Weak density of smooth maps for the Dirichlet energy between manifolds. GAFA, Geom. funct. anal. 13, 223–257 (2003). https://doi.org/10.1007/s000390300006

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  • DOI: https://doi.org/10.1007/s000390300006

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